The gemara says that Yoshiyahu hid the Aron (and the other items i.e. tzintzenes ha'man, shemen ha'mishcha...) because he understood from th Torah that the Jews were going to go into galus. This is learned from the pasuk in divrei hayamim from the pasuk - תנו את ארון הקדש בבית אשר בנה שלמה בן דוד מלך ישראל. The Rambam (Hil. Beis HaBechira 4:1) writes - ובעת שבנה שלמה את הבית וידע שסופו ליחרב בנה בו מקום לגנוז בו הארון למטה במטמוניות עמוקות ועקלקלות ויאשיה המלך צוה וגנזו במקום שבנה שלמה
There was a stone in the kodesh hakadashim on which the Aron was placed. At the time Shlomo built the beis hamikdash he understood that it was going to be destroyed and therefore built into the structure a place to hide the Aron. It was Yoshiyahu who realized that it was time to follow through on Shlomo HaMelech's initial plan and to hide the Aron. The Rambam cites the pasuk from our gemara. The Tosafos HaRosh (on the side of the gemara) explains that the Aron was already in the mikdash. Why did Yoshiyahu have to say that it should be placed in the bayis? Secondly, why does the pasuk reference Shlomo HaMelech? Clearly, the pasuk is indicating that Shlomo HaMelech initially understood that there would need to be a hiding place built underground in the beish hamikdash where the Aron can be hidden.
The Tosafos HaRosh continues, perhaps the pasuk in Melachim (1:8:21) which says - ואשים שם מקום לארון, refers to this hiding place. Shlomo designed a place for the Aron to be hidden and it was only revealed to very few of the kohanim and leviyim which is why Yoshiyahu spoke - ללוים המבינים לכל ישראל הקדושים להשם which means he told those who had a tradition about where this place was to hide the Aron in that place.
The Meshech Chochma (haftorah on pekudei) suggests that the pasuk of ואשים שם מקום לארון is not a reference to the hiding place, rather it is a sanctification of the place where the Aron stood in the kodesh hakadashim to give it the same kedusha as the Aron itself. He references the Rambam that Shlomo HaMelech understood that at some time in history the Aron will not be in it's proper place, so he sanctified the place of the Aron so that the sprinkling of the blood and burning of spices can be done on Yom Kippur even in the absence of the Aron, as if the Aron was still there. The Meshech Chochma at the end seems to agree with the Tosafos HaRosh (without quoting him). The reference to the "place of the Aron" is actually the hiding place that was designated for the Aron right beneath the kodesh hakadashim so that even when the Aron is in hiding, it is still במקומו - in it's place, to allow the avoda on YK to be done.
The Brisker Rav (letters printed in the back of the sefer pg. 81) was asked about the halacha that in the absence of the inner miz'beiach they were able to burn ketores (incense) in the place where it stood (zevachim 59). The Brisker Rav writes that the place of the mizbeiach had the same kedusha status as the mizbeiach itself, just as the meshech chochma suggests about the Aron. I once heard a fabulous shiur from Rav Nota Greenblatt from Memphis (given in our beis midrash) where he disagreed with the Brisker Rav and proved that that the halacha of ketores is not on the mizbeiach, rather on the makom mizbeiach. Meaning, it wasn't necessary to give the place of the mizbeiach the kedusha status of the mizbeiach because the halacha of ketores was on the place, not on the mizbeiach.
According to the approach of Rav Nota that the ketores doesn't require a mizbeiach so there is no need to say that the makom of the mizbeiach had the kedusha of the mizbeiach, there is a difference between the mizbeiach and the Aron. The halacha of burning ketores and sprinkling on YK in front of the Aron is that when the Aron is hidden underneath the ground, kedusha still emanates from it to sanctify the place where it stood as if it were there. This is very meduyak in the mishna Yoma 53a. The mishna refers to the Aron and to a Paroches. The gemara asks that the two never coexisted. In the first mikdash there was a wall and no paroches. In the second mikdash there was no Aron. The gemara concludes that it is referring to the second mikdash, so when it says "Aron" it means "makom Aron", and when it says "Bein Habadim" (between the poles) it means as if it were between the poles. Since the halacha of burning the ketores and sprinkling require kedushas ha'aron, the mishna talks as if the Aron was still there even in its absence because the kedushas ha'aron was still there.
After discussing this with R. Nota again (11/21/10) he pointed out that the gemara in menachos 27b explicitly says that the ability to burn ketores and do haza'os in the second beis hamikdash was a result of the kedushas hamakom of the aron. The only question would be whether this would require the aron to be hidden in the place that Shlomo designated for it, or whether the makom had kedusha even if the aron would be in the hands of the pelishtim. The simple reading of the gemara implies that it is simply a din in kedushas makom of the aron even without an aron.
M'inyan L'inyan here is the summary of the shiur:
The Torah never refers to the mizbeiach inside as the מזבח הפנימי (that is loshon chazal), rather it is called the מזבח הקטרת (burning spices was everyday whereas the sprinkling dam ha'par was once a year). BUT after Betzalel makes it (Parshas Pekudei by revi'i), and places it in its place it is called מזבח הזהב. Why is it not called מזבח הקטרת in that one place?
In Parshas Vayikra (by par kohein moshiach) the Torah returns to call it מזבח קטרת הסמים. The Mishna in Menachos 49 says that only ketores works to be me'chaneich the mizbeiach, not with sprinkling the dam of the cow. In Parshas Vayikra regarding the sprinkling the dam of the cow on the mizbeiach, the Torah says it should be sprinkled על קרנות מזבח הסמים אשר לפני השם באוהל מועד. The gemara in Zevachim 40 asks why does the Torah have to say על קרנות מזבח הסמים since it already identifies the inner mizbeiach and not the outer by saying אשר לפני השם? The gemara answers that the sprinkling can only be done on the mizbeiach after it is nis'chaneich through the ketores as the mishna says in menachos. Meaning, the pasuk writing "mizbeiach ha'samim" is not to identify the mizbeiach, rather to tell you that ketores must be done first to sanctify the mizbeiach. The mizbeiach isn't essential for the burning of ketores as we see in zevachim that the ketores can be burned in the makom of the mizbeiach even in it's absence. Why is it called mizbeiach haketores? R. Nota explains that it is called mizbeiach haketores because that is the only way to be me'chaneich and sanctify the mizbeiach. Therefore, after the mizbeiach is made by Betzalel, before it was used, the Torah in Pekudei calls it מזבח הזהב because until it was nis'chaneich through ketores it couldn't be called the מזבח הקטרת. Only after the mizbeiach was nis'chaneich through the ketores could it be called again in Vayikra מזבח הקטרת.
The Brisker Rav held that the halacha of burning ketores in the absence of the mizbeiach is because the place itself had kedushas mizbeiach. The Meshech Chochma (Pikudei on the pasuk of mizbeiach) goes one step beyond the Brisker Rav. He agrees that the the halacha of burning ketores in the absence of the mizbeiach is because the makom itself has the kedushas mizbeiach. He continues by saying the din that when the mizbeiach is missing the ketores can be brought in the makom, only applies in the beis hamikdash but not the mishkan because in the mishkan there was no kedusha to the place of the mizbeiach. Now, if the Meshech Chochma is correct, the mizbeiach in the mishkan was actually essential for the ketores and that is the more obvious reason for it to be called mizbeiach ha'ketores (not necessarily because of chinuch). According to the Meshech Chochma the question would come back - Why would the Torah call it in parshas pekudei מזבח הזהב and not mizbeiach ha'ketores since the ketores is essential for it.
Rav Nota argues that the Brisker Rav and Meshech Chochma are wrong in assuming that you need a mizbeiach for ketores just that the place of the mizbeiach has status of mizbeiach (which allows the meshech chochma to differentiate between the mikdash and mishkan). He argues that the torah describes the halacha of ketores in Parsha Ki Tisa to be ונתת ממנו לפני העדות באוהל מועד, implying that you don't need any mizbeiach at all for ketores, so long as its burned in front of the Aron. Therefore even in the mishkan the din is true that you can bring ketores even in the absence of the mizbeiach so long as the ketores is being burned לפני השם - in front of the Aron. According to this approach, the inner mizbeiach is not called מזבח הקטרת because it is essential for ketores, it is not essential even in the mishkan. It is only called מזבח הקטרת because that is what is necessary to be mechaneich the mizbeiach. Therefore, it makes perfect sense that in one place in the Torah (Parshas Pekudei), after the mizbeiach was constructed but before it was sanctified through ketores that it is called the מזבח הזהב.