This old laptop (Or how can I cool down a CPU without operating it in a dry ice tub?)

Yeah a lot of P4 processors are built under the Prescotti design, and those love over-heating. I'm not sure what to say if you can't find some kind of good deal in purchasing a fan. I know purchasing an "anything" for a laptop will be considerably more expensive than for a desktop, even fans. So yeah, I'd get that fan if it'll "fit" appropriately over having the laptop die in the end.

Also, see if you can open up the laptop all over and air-spray out all the potential dust. I happened to just look at my notebook's parts when replacing memory sticks and there was dust hiding all over. That notebook stand can also help, so could an actual FAN-fan, but these are all temporary solutions.

Jam it back in, in the dark.