How's your coolant level? If the coolant level is OK, I would suspect a worn fan clutch. With the engine off, there should be resistance when you try to turn the fan blades. DO NOT under any circumstances attempt to stop a moving fan! If you can move the fan easily, it needs to be replaced. You really only need the fan to cool until about 30 MPH, after that the flow of air through the radiator does the job

Turning the heat on when the engine is running hot is an old trick to limp a car home when over heating. That starts dumping heat from the cooling system into the passenger compartment, sort of a heat transfer operation, which buys you a little time. Not something I would suggest doing on today's cars, with aluminum heads and/or blocks.

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Mike Tangas
73 280 SEL 4.5