03 cruiser radio power problem

I am perplexed with a radio problem. My radio works intermittently and for no apparent reason will shut off. I replaced the radio and the same thing is happening. Could this be a relay issue? Is there a relay that controls power to the radio? It seems like it may be related to heat. When the car is cold it almost always works, for 5-10 minutes and then shuts down. Then, if you turn it off, after a period of time it the clock will come back on. Turn on the radio and get another 7-10 minutes.