Hi again rockmouse.
The difficulty is that laptops really are not laptops; meaning they are not for laps. Some of them are too large and heavy anyway for the lap, (my Packard Bell for example I could never use on my lap), but the problem is heat.
Laptops don't have the number of cooling fans that Desktops do, and they have to use different ways to dissipate heat. Heat is the processor killer, and motherboards are designed to shut down if they overheat to prevent damage to the processor and the rest of the electronic circuit board and hardware.
Many laptops have vents on the underside but when the laptop is sitting in the lap, the vents are blocked and cannot circulate air and remove the heat. You say you have noticed this yourself when it starts roasting your leg. That's a danger sign, not just for your leg, but for the laptop itself, and, if I may say, placing it on a cushion is only going to make matters worse.
A table or desk is best, or some other hard surface top. Have a look at Bob's advice about cleaning laptops in the link below. All laptops are different of course, but in all cases, vents can get blocked by dust;
http://forums.cnet.com/7726-19681_102-3196452.html
One more thing. How old is the battery? As a general rule, laptop batteries are good for about 300 cycles, (fully charged > empty > fully charged is one cycle), or 18 months to two years. Batteries can overheat as well and should only be replaced with the makers recommended make and model batteries, not cheap ones. I'm not saying the battery is the cause of any overheating, but a bad battery can overheat.
Laptop cooling pads are also available, examples at http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=Laptop+coolers&x=0&y=0
Hope that helps.
Mark