A thermal fault in a chip is a pretty lucky kind of fault to diagnose. You know the PCB works fine when it's cold, but not after it's warmed up... That gives you an easy way to test it.
Leave it on until the fault starts appearing, then cool each chip on the PCB one by one and watch if it makes the fault go away. Once you find that cooling chip X makes the problem go away, you know chip X is the problem and needs to be replaced. No special testing equipment needed, no having to follow traces on the PCB, schematics or looking up datasheets for every part.
A can of Freez It/Freeze Spray/Super Freeze/Arctic Blast/etc... is an aerosol can you can buy at most electronics shops. It sprays cold. You can spray it on a chip while the board is powered up...
*...but rapid temperature changes to a chip (whether powered or not) can on occasion trip a chip from "marginal" to "faulty".
It sounds like the problem could be either of two things:
The power supply is under-voltage and the voltage drops too low after it warms up.
Or there is a thermal issue with one of the chips on the PCB and it falters after it warms up.
