First thing I'd do is reset the SMC, which may just have its signals crossed a bit. If that doesn't work, make sure you don't have anything like smcFanControl installed. That program may be useful in a limited number of diagnostic applications, but it shouldn't be used regularly. It can lead you down a dead end road when trying to sort out problems. So make sure any programs you have only monitor fan speed, not control it.
I'd be surprised if resetting the SMC doesn't solve it, but if it doesn't, then I hope you have the Apple Care plan on that system, because you probably have a logic board on its way out. That will run you several hundred dollars, and usually isn't economically worthwhile. Why spend $500-$600 to repair a system when for $1,000 you could get a brand new one, with better specs, and a one year warranty to cover these kinds of repairs?
MacBook Pro 2.16 Intel Core2Duo with 2 GB 667MHz SDRAM runs very quietly when being used. When left with lid closed overnight but still logged in, each AM the the fan is running loudly at high speed and the case is hot. As soon as I open it and it starts up, the fan quiets down and the case is cool in a few minutes. The temps range (when open and quiet) from 90-125 F for various components and the fan speeds are about 2000 RPM. Why should it run hot when closed and asleep.