My FP2 is also getting very hot above the battery (right of the camera), but I thought it comes from watching videos, for example on youtube. Not shure what module lies there
It also drains the battery a lot, but I don't think it's empty as fast as yours.

Perhaps its just a browser issue with html5 players... but since my FP2 can't play back video files from "disk" I cannot confirm my guess.

Edit:
After clearing my gstreamer cache (https://github.com/ubports/ubuntu-touch/issues/661#issuecomment-401391699) I could confirm, that my FP2 is overheating on html5 playback.

I played the same video with UTmedia app (html5 player) and with native media player:

html5: gets very hot, nearly untouchable native: gets warm

So for me, I suggest it has something to do with hardware acceleration not working for html5.
Otherwise, if @Danceswithcats did not play back any media in the browser, this could be a general issue in the webapp(-container).

btw: I'm on 15.04 ota3.