The electric fan you speak of has been part of my: “Things to do for summer operations” checklist for years now.

Every year, when the temp hits and holds 80+ during the days, I unplug those two wires from the dryer switch and place a 15amp blade type fuse across them. I just leave the wires from the switch tucked out of the way. Not sure if that’s the right size fuse for the fan or not, I just had one handy one year and started using it. It winters in the glove box. Same fuse. Same fan now, for the past 5+ years.
All summer long - When the key is on - The fan is on.
Does not seem to ill effect glow time and starting either.
I go back to the OEM set up around September/October.

I’m sure the pros here will find issue with doing this, but it’s worked fine for me for many a hot N-TX summer. Never been over 100c in any type of driving. I leave the A/C on Auto-HI and the dial at 65 too. (But then, I’m running 134 now. Not as efficient as R12, I hear.)

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1980 300D - Veggie Burner !