i just use an Incase, I like the grippy feel of it, and a screen protector on my latest iPod touch. Doesn't get hot. I don't play demanding games on it and don't keep the WiFi on for very long at a stretch, usually, so your experience could vary. It never gets hot sitting in a speakerdock, even playing music for hours. It does not get hot charging off an adapter and USB cable.
An Incase case does protect the device nicely from a corner ding if it falls off a table. The slightly raised rim of the casing seems to protect the screen OK if it falls face down, too. I have used various models of them on the first iPod touch, on iPhone original and iPhone 3GS.
One of the ones I had for a 1st-gen iPod touch got a little rip in an upper corner, not sure why, possibly the room was very cold and dry at the time. The case still protects enough but the rip does show a little bit because that case is bright yellow. Anyway now I really try to ease the things off the corners very carefully when removing them for cleaning.