Yes, heat is an issue.
My Toshiba came with warning labels "DANGER" heat, sort of thing. And it can get very hot. In the winter I felt it was a good little heater.
I have mine on an old refrigerator plastic shelf from my small refrigerator. It has lots of little - darn, I don't know how to describe it... but it is so that there's a lot of air under my laptop.
Then a month or so ago my computer quit and I took it to a fellow in town rather than send it away, since I need it so much, and he turned down the brightness of my screen and now it runs a lot cooler. Who would have guessed.
(My screen still seems real bright, so it isn't hurting my enjoyment.)
Oh, Brian, I almost forgot to say... mine is on nearly 24/7.

not quite... but pretty close sometimes.