The heat isn't magical. It just affects the expansion or contraction of metals. If you have a cracked solder joint on your plug pins, for example, it may not work when the game starts and the metal is cold. That's because the crack is preventing a good connection between the board and the pin. But, once you heat it up some, the metal expands on a microscopic scale. It may not seem like much, but it can be enough to make a steady connection between two otherwise unconnected points. The same thing can happen with a failing component.
In the meantime, I'd try wiggling plug J137 on your power board, and see what happens. If your lights change state (go from working to not or not working to working), it's a good sign you probably have a cracked solder joint on pin 1.