Since we are talking about air cooled mowers (not mountain roads or forklifts), the fan is directly attached to the crankshaft, so if the engine is 1000 rpm, so is the fan.
On an air cooled car (VW), the fan is attached to a belt and pulley, so while the engine is at 1000 rpm, the fan is spinning much faster at 2000-3000 rpm. Thus moving a lot more air at idle than a direct drive lawn mower fan.
On an air cooled car, there should be sufficient fan spinning at idle to cool the engine. On a direct drive lawn mower, there likely isn't sufficient air movement at idle.
Idling a lawn mower engine is not the best for it. The fan and the splash oiling system is designed for 3100 rpm. Not 1000 rpm.
As to the OP's question, why do we care about cooling? Run the engine as designed, keep the cooling fins free of dirt/debris, and maintain it with new filters and an oil change every now and then and it will give you long life. Why do we need to care about its temperature? Its not likely to overheat unless we abuse it beyond its design limits.