When the board is powered on, and all circuits are a GO, tempature rises in the board, expanding components to make possibly better connections. It's quite possible, somewhere, some of the PCI/AGP boards, RAM, anything aren't seated completely. Or if there's some kind of line break on the board, when it heats up it may expand to make better continuity.

Open up the system, try reseating the video card, the RAM, and any other boards on there. Make sure cables aren't pulling the video card out of its socket.