IOS – iPhone 4S chip overheating after replacing screen

In my experience, if you're on a dual-GPU MacBook Pro and running 15 Flash sites, quick battery drainage is almost expected. Even if you installed something like ClickToPlugin, which replaces YouTube's Flash app with QuickTime and is more efficient, the computer should still be fairly warm or borderline hot.

You should use something like gfxCardStatus to verify whether any of the open apps are forcing a switching to the Nvidia GPU. If there is one issue that is often associated with high temperatures and fast battery drainage, this would be it. Try closing the affected app and see if things improve, and then try figuring out a way to avoid the GPU switch (which may entail replacing the app by another one which is better behaved with respect to GPU switching).

Take it to Apple.

Electronics & water do not make the best of bedfellows.
I wouldn't consider a day in rice to really be sufficient to ensure the inside is not still wet, or otherwise contaminated.

I also sincerely hope you threw away the rice & the hot press afterwards.