Sounds like a cracked trace (those metallic lines that go all over the place) on the mainboard. Heating causes things to expand and thus electrical contact is made. Traces can be broken by pressing too hard down on the board while installing RAM, plugging in connectors, etc.
I had one client whose board was cracked by the RAM sockets and would not boot. I first tested it by gently pressing with something non-conductive under the board until it booted. Now I knew where the problem was. I fixed it by gently stacking 30mm rubber case feet on the side panel on the mainboard underside side so that when you re-install the side panel it pushes gently up on the mainboard. If you stack too many you could risk pushing up too much and cause more damage. So move slowly and carefully. I added one at a time until it works reliably.
This may not be the solution for you but may help others. Good luck!
Oh and for future questions it really helps us a lot to help you if you give the exact mainboard model you have. We can then look at the user/service manual and give more informed answers. Thanks.
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