I agree it would be nice to run a fan, but not in this scenario.

The only time running a "hot" engine is preferable is if you are overheating due to load, but still have water and a functioning fan. Then idling will lower the temps better (and safer) than shutting the engine off.

Even then, if you are near redline, just shut the engine off and open the engine bay and let ambient air do it's work.

Then pray and pray some more that you don't have thousands in repairs.