Its always difficult to diagnose problems without having the thing in front of you and hearing or seeing whats going on. The fact that it improves with time or warm up would kind of point me in the direction of Voltage / Current or a Thermo issue in the PSU or Amp itself.
For me, first thing I would be doing is measuring the Voltage Output of the PSU against its spec and does that change with time / warm up, also if possible look at the current feed, if that proves difficult to do, then easiest way would be to look at any Voltage variation under high loads that should give some clue as to stable the PSU Voltage vs Current supply is doing. Faulty or deteriorated Caps could or would upset the Voltage / Current supply.
Assuming the PSU is doing its Job and that fact that the Amp works but changes with warm up I would then be looking at similar issues within the Amp, Firstly correct voltage and current supply to the Amp and within, as said, Connectors, plugs, switches, dry joints etc, and then move on to see if any thermo coupling design within the Amp is a problem, is the Amps Output Heatsink getting too hot or Cold, without knowing the design is there any Thermo Sensing around the Heatsink or Output Stages or has any Components attached to the Heatsink with Silicon Heat Sink compound, has the compound over dried or powdered through age.
Good tools for this, would be Decent Volt Meter, Hair Dryer and a Can of Freezer, and Ideally a good Oscilloscope.