Sometimes aftermarket fans don't spin as fast as the machine's "detection level", so a slow spinning fan looks like a dead fan. It's always nervous to turn OFF a fan indicator, cause you'll have no idea if it ACTUALLY dies on you. Granted though, should the fan die, as long as you have your thermal detection set for a decent temp (like 60-65C), then the computer should shut down far before the temp of chip damage, and only then would I disable the fan warning.
If your BIOS doesn't provide for thermal top ends, then I'd suggest changing the fan on your HSF to something that spins a little faster (doesn't have to sound like an F-14 engine), or live with an occasional warning in trade for the safety net of the fan monitoring.