Comment:: Laptops are engineered much smaller than desktop PCs. Therefore, you've got your battery, your hard disk drive, your optical (CD/DVD), possibly a floppy, and then the motherboard and the processor. Also, the faster your processor's clock speed is, the more heat it generates.
As a rule, I would completely refuse any notebook not coming with some air vents, and would think twice on a purchase of a book w/o a fan. Does your notebook have a fan?
The startup/shutdown may have nothing to do with heat. Consider viruses,
low batteries and operating system malfunctions.
If it is heat, and you don't want to dump your laptop, consider this: You will be using less heat using AC power rather than battery power whenever possible. Batteries tend to act as a radiator, radiating a lot of the heat you feel throughout the apparatus. Also consider underclocking your CPU a bit if you aren't a speed demon.
Also take into consideration that, if it comes down to motherboard replacement in a laptop, it almost always comes down to whole machine replacement. For these reasons, and because laptops are shorter lived than desktops, I wouldn't trust a laptop as a primary machine.