Sounds like a MB or Processor problem for sure - probably overheating related as you surmised.
For future use it's well worth getting one of these fault finding cards at about 1.50 delivered.
DealExtreme: $2.57 PC Motherboard Repair/Troubleshoot Boot-Failure Diagnostic PCI Card
Basically put in PC, switch on, read code and it should give you an indication of the faulty hardware.