In electronics heat is often The enemy. In valve amplifiers there is a tension between this basic rule and the valves themselves which get mighty hot and also the established design methods for amplifiers.
The problem is that heat damage caused by power resistors and valves eventually changes the circuit board material from a good insulator to a partial conductor. This damage is not reversible.
The burns do have to be quite severe mind you. You will usually see inner layers of fibreglass exposed, carbon particles. The only real cure is removal of the effected area. For small areas of damage the effected area can be drilled out but for larger areas a section may need to be cut out.