But, what if there is no coolant left to circulate? Idling would let the fan blow, but maybe stopping and opening the hood would be better in this case.

I guess it depends on if you know what has happened under the hood.

I drove a vehicle once that had less than 1/2 its coolant. The gauge read full cold until I hit a bump and sloshed some around then the sensor would jump. Luckily it was -20C out!

1991 Mitsubishi Pajero XP TD LWB family hauler.