Another consideration could be either the power supply suddenly deciding to stop supplying power, or that the mini's fan has broken. It's easy to get temperature issues inside a case that small, and if the fan isn't moving, neither is the air.
I'd start with an SMU or PMU (I can't remember which the mini uses) reset, then verify that the minis fan is working by running 'yes > /dev/null' in the terminal (If you have a dual-core machine, start up a new terminal window per core) This will cause the CPU to heat up, which should also cause the fans to ramp up proportionally.
In general, you should strive to stimulate the failure, then troubleshoot the cause.