Firefox Makes My Laptop Fan Run Constantly

When I use Firefox the CPU meter goes way up, and the fan runs constantly. Sometimes when I am watching a YouTube the computer just shuts itself off. If I run Firefox and Skype at the same time I have to anticipate the shutdown.
Does anyone else have this problem?
I have a fairly new HP laptop with an AMD dual-processor. This happened in Windows Vista and now Windows 7. I really don’t want to have to switch back to IE and Safari isn’t quite there yet…
Others have written about this problem: Firefox: Heat and the CPU usage problem