After a computer is turned off for a period of time the actual temperature of the system is dictated by the ambient air conditions in the room that it is in.
When you turn on the computer, the temperatures of all the components begin to rise and as a consequence begin to expand. As this expanding takes place, any part of the computer which has any type of flaw may fail briefly or completely. This can include virtually any component in the system, from the power supply to the smallest of motherboard tracings including all solder joints.
It seems, and this is only a guess, that once your computer gets past this critical warm-up event, that whatever component is having the problem reaches a temperature that permits the connection or contact to re-develop and allows the computer to continue to operate without error. I suspect that that is why all subsequent reboots (warm boots) do not produce the problem. Such a problem is difficult to diagnose and would require the exchanging of multiple components starting with the power supply, one at a time until the problem is resolved.
The bad news is, whatever the problem component, it will likely fail completely sometime in the not to distant future. The good news is, at that time it may be easier to identify the faulting component.
Best Wishes and Good Luck
Randy