Now THAT'S a Spinner!

[Dana]

I doubt the claim because the advantage of the rotary engine's success
was improved cooling: when the engine was running, the rotating
crankcase cylinder assembly created its own fast-moving cooling
airflow, even with the aircraft at rest or sporting a spinner...

Spinning the engine helps, but you still need to have cool air coming in. If the engine is spinning inside a box of hot air, the air will be circulating but it won't do much cooling.