I am running Linux on a laptop with a major problem. Basically the heatsink is not sitting on the chip properly and the machine overheats very easily.

I want to compile an updated kernel (or if this solution still applies during a fresh install, may even want to do an FTP install of a new distro from scratch). I just can't let the cpu run at anything near full capacity for very long.

'nice' seems like the best way to go, but I couldn't tell from the documentation I read; If I deprioritize my 'make' command will it run with less demand on the chip? Will there be intervals where the job is paused completely? The man pages make it sound like 'nice' is only deprioritized relative to other processes. My impression is that if I don't have much else competing for CPU time, then 'nice' won't have any effect at all.

Is there a different command I should be considering here?

Well, I know that nice is not what you need to use. Nice prioritizes existing processes, however I don't think it is capable of throttling CPU usage. Essentially if you have a single low priority process running, it would get 100% of the CPU time, just because there is no competition.

I've never done it, but from doing a little googling, I've seen references to using ACPI to throttle back the CPU speed. I found this site which explains it in a bit more detail.