I'm not entirely convinced that the problem is only indexing.
My 15 Pro (not Max) is sitting at pretty much normal room temperature when not in use, but I just spent about 10 minutes watching streaming video over wifi with the screen at about 30% brightness (in a room with a temperature of 69 degrees fahrenheit, so it's not an ambient temperature issue either) – the phone got hot enough that it was uncomfortable to hold, and the battery dropped by about 15% in that time (not exactly the "up to 23 hours" of video playback time that Apple claims there...).
I'm not going to say that indexing couldn't be part of it, but 1) that seems pretty extreme, even with indexing, and 2) I would hope that Apple throttles their indexing when the phone is busy doing other things.
I'm going to give it until the end of the week for indexing to finish or for Apple to release a software fix or whatever, but if it's still doing this by then, I'm returning it. I'm also recommending to friends who haven't gotten their phones yet to hold on buying anything until we see where this goes.
(Oh, and in response to the other post, it's a 1TB phone with about 600GB free, so it's not a free space-related issue either.)