My KRV-7070 shuts down when it gets too hot. It is either off or on, so your problem is interesting. You didn't mention whether the receiver's built-in fan was working. They can fail, as can the circuitry that turns them on. Also, check that the 8 ohm/4 ohm switch is in the proper position.

Finally, make sure there is adequate ventilation around the receiver. Nothing should be placed on top of it. In fact there should be at least a couple of inches above it, on both sides and behind.

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.