The fans are electric in the FEH and can and DO run even when the key is out/engine is off if the system is very hot.

The coolent pumps are electric and will continue to circulate the coolent even with the engine OFF ( not sure if they will with key out ).

DO NOT do what the previous posted suggested ( force engine to stay on ).
This is totally UN-needed and will waste gas.

Your FEH will cool off quickest in EV mode, key on. For Sure.