Ta'anis 13a - Tevillah in Warm Water

The girsah in our gemara is that there can't be tevillah in warm water since it will inevitably be drawn water which is pasul for tevillah. Although both Rashi and Tosafos were not gores in the gemara "h'a sheuvin ninhu" - they clearly both explained the gemara that the problem is that all warm water is sheuvin. This gemara seems difficult in light of the gemara in yoma 34b that says that they would warm the mikvah water for the kohen gadol using hot metal that was heated from before yom kippur. Clearly, it is possible to warm the mikvah without rendering it sheuvin! Perhaps the answer is:
There is a reference in the hagahos ha'gra to his comments in Y.D. (201:125) where he seems to use this gemara as a support to the opinion who says that you cannot immerse in warm water even if it was poured into a mikvah after the mikvah is full [40 seah +] (so that the drawn water will not passul it) bec. it looks like a bath house. According to this approach, the issue is not that it is impossible to have warm water in the mikvah unless it is drawn, but rather the issue is that warm water resembles drawn water and is assur bec. of the appearance of a bath house. Based on this approach the issue in our gemara is not that it is actually sheuvin, but rather warm water looks like a bath house and therefore is "like sheuvin".
This explanation can be supported by the cheshek shlomo who points out that in brachos 22a the gemara is discussing the immersion of a b'al keri where actual sheuvin is not a problem (see beis yosef 88), yet there is a problem of warm water - clearly the problem is that it will be confused with a bath house and will lead to immersion inside a vessel itself which is prohibited even for a b'al keri.