I realize I am reviving a slightly old thread, but wanted to post my experiences and also see how others are doing now with more rMinis in circulation.
I have a 64GB Verizon rMini. It gets warm, but not hot, after moderate usage on WiFi or on LTE, on the back towards the bottom/right side. This is with about 40% brightness. This comes with just internet browsing, email/iMessage, reading Newsstand etc. No games or other highly graphic intensive apps.
However, I have had my rMini with the screen off streaming HD video via AirPlay to my TV for several hours today and it is completely cool to the touch. So I guess this would mean the screen is the most likely culprit?