I'm looking for a way to explicitly limit how much cpu percentage a program can have access to. This probably seems a little odd, and normally it wouldn't be a problem, but in this case I'm having issues. Most chess programs, such as gnuchess, are built to use up to 100% of the cpu's capacity to compute moves and such, but on my laptop this pushes the heat up to unacceptable levels. The processor's already underclocked to its lowest setting; I was hoping for some way to limit the program to treat my processor as a 500mhz or something like that.

If anything like this exists, or if you can suggest any other solutions, I'd really appreciate it. I hate not being able to play chess on the go.

Have you tried 'nice-ing' the program? NICE is a level of priority which any given program can have.
19 is VERY NICE (low priority) and -19 is NOT NICE (Hog the machine: high priority).

I'm not absolutely certain this will give you the result you want, but it's worth a try. If you start GNUchess from a console, or from like a desktop icon, use the command like:
nice -n # gnuchess
where the # sign is a number from -19 to 19 and 'gnuchess' is whatever the actual command/path you use to start the game. (try 19 for the maximum effort at nice-ing it -- though *some* things won't run if they are 'too nice') and note -- some 'nice' settings require you to use root priveleges. You may want to start the game as USER, then use ROOT to re-nice the process.

cpulimit should do what you are asking for.

Thanks, cpulimit works perfectly.

And thanks for the reminder about nice values, I had forgotten that. They're coming in handy for some other things I needed done.