Depends on the cat. Assumpta used to be pretty indifferent to temperature, but since the pancreatitis thing, I've noticed she has a much higher tolerance for hot weather and crowds the stove when it's cold. Some cats are heat-seekers, others like cool spots. Just a note, though: cats are very poor judges of how hot is too hot, and they often don't realise that they're burned until it's already happened, so caution around heating pads, fireplaces and stoves is prudent.
As for mice...well, I USED to think Assumpta was bringing me gifts because I was the "big cat." Since then, I've watched her closely, and she always runs around making the mommy-cat "murf...time to eat!" noise, and tries to forcibly feed me the mouse if I don't come when she calls. So I've come to the conclusion that she just thinks I'm a big, stupid kitten...what a letdown.