[kwilford]

Is it possible that the relay energizer circuit (the wire that ends at terminal 85, which normally provides power to the solenoid in the relay via the headlight microswitches) is being powered through the parking lights? Some folks do that when the microswitches fail, and simply power the relay with the parking light switch. If so, then no worries, as the relay is actually taking the headlight load. But if the headlights themselves are bring powered through the parking light switch and NOT through the relay, you are about to experience a melt down as Ron has suggested.