teh C3LL can cool itsself and the rest of the console down.
It has no limits. You can even play games you dont have because of teh C3LL, just ask
Gearbox

The important question is if it will have an internal power supply.

That might answer this question.

japanese things don't overheat. everybody knows that

well at least not a rate over 33%. :P

The PSP should be over heating as well, PSP slim that is, a machine less than half hte size of a PS2, and has a screen, and has PS2 quality graphics..

Smaller chips = less power consumption and heat = no need for fans of the same size and CFM rating.

Lol, this is a weird question. When a slim-line system comes out, they don't just cram all the current hardware in the regular system into it. The whole point of the slim is that technology and manufacturing methods have improved so that the system can be made smaller, generate less heat, and fit in a smaller case. Heat isn't an afterthought, it's part of the design.

No.

Does any console on the market today have a tendency to overhead?

No.

That´s a good question. My ps2 slim becomes much more warm than my fat ps2. Sometimes i even can not touth  it!!

The voltage regulators on the HD 4870 can exceed 100 degrees C, and yet the hardware itself is operating within normal parameters.

You rock!