If you have narrowed down that your motherboard is faulty you need to replace it. Repairing the motherboard is not to practical. Chances are if your motherboard is bad its probably outdated anyway. Read carefully and see if this is your system. Burn Baby Burn -Overheating, the motherboard does have a tendency to go bad in warm situations.
Heat is the ultimate killer in any system and to any system component.
A little heat is fine but to much can be a problem. What normally happens with a motherboard is small cracks in trace wires and chip creep. This is from the motherboard heating up and cooling off. After time this expansion takes its toll on the board. Having one fan mounted somewhere in the case along with a CPU fan can really cut the heat down.