I was having the same issue with my phone, a Droid 2 purchased Jan 2012. Didn't change usage, settings, etc. Got VERY hot, sometimes while charging, sometimes just while idle. Hot to touch hot, not just warm. Battery also began draining so it wouldn't hold a charge reliably...sometimes only a couple hours with little to no use, after being able previously to go 3 days without recharging. I use very few aps. Took to Verizon store where service rep reviewed aps and usage, changed some settings, said try for a week or so and if no improvement, they would likely give me new battery to try; if that didn't work, they would likely replace the phone as they have been having issues with this phone. The settings changes made NO difference. Went back to store about 10 days later and repeated service/battery/problems. This service rep skipped new battery step and just put in for a "new" (refurbished) phone to be sent to me. Today I'm in the process of setting up the new phone which came via mail. It would not set up automatically following screen instructions, but customer service came on the phone and did something from their end that allowed me to continue the activation. Now my phone is working...sort of. It will not allow my yahoo.mail account to load as an app. so I can't access my email (main reason I'm paying for this phone/plan.) Have tried a dozen times including closing my inbox on my computer, restarting phone/email install from first screen and re-entering name/password a bunch of times, and everything else I could think of. Tried camera, which works, but is "grainy" compared to my first phone, and pictures are not re-sizing/acclimating to direction of screen (tall/wide view) to allow for bigger viewing of picture as before. Guess it's back to the Verizon store for 3rd time unless someone has some help here. I would also be leary of a hard reset without more info.
My usage has not altered either.