Class A receivers such as this are designed to operate in a very inefficient portion of the amplifier performance curve, and then naturally generate lots of heat. Your unit is heating to the point that the amplifier is operating in another region of its performance curve, causing the distortion. I suggest the right place to look is in the final amplification stages, which have large transistors with large heat sinks. Go to Radio Shack and get their cooling spray for troubleshooting, then, when the distortion presents itself, spray one of the transistors (not all) and listen for the distortion to go away. Do this until you find the offending circuit.
Once you've found the circuit, the advice changes. Can you solder, without damaging surrounding components? As much heat as one of these power transistors needs to remove it, there's a danger of delaminating circuit board runs. Be careful.