The answer I got from Sony was to do a software repair. Haven't had time to do that yet but will this weekend. They said also that if that did not work that I could take a copy of the mail I got from them and the phone into a Sony service center and have them check the phone out for possible fault.
I am encouraged by the folks talking about undervolting. Makes me think that this could be solved with some firmware adjustments.
Tried to do it. Not helping. Had the same suggestion from Sony guys.