This sounds very much like a cracked pin or wire between the head unit and the amp. The problem is proving it.

In the cold, when you warmed up the car and got to where it was over 60 degrees for 20 or 30 minutes, did the problem clear up? If my theory holds water, then as the components and cables warm back up, the damaged pin would expand and make better contact.

Anyway, just my $0.02

Larry