I would run the Apple hardware test to see if there is a sensor issue. Run the extended test when prompted, which can take over an hour to run.
If your system came with OS X 10.6, then use the original OS X DVD that came with your system. It will say 'AHT Version x.x' in small print on the label. If it came with OS X 10.7 Lion, follow the directions in the Apple note.
Sorry for delay getting back to you .... See steps outlined in this Apple note for systems that won't start. While yours eventually starts, see if any of the steps in the note help you. Otherwise, you may have to take it in for service.
When asking you to run the hardware test, I was hoping it would show up with a bad temperature sensor. Of course, if the system were genuinely overheating, that could account for a delay in turning it back on. There are several programs available to tell you the system temperature.