250cc engines in scooters don’t work nearly as hard as they do in motorcycles. The Kymco Bet & Win 250 is quite happy at 75mph. As for cooling, most scooters larger than 150cc are liquid-cooled now, and the air-cooled scooters have cooling fans and can be run all day at any speed.
The guy I was posting to was looking at 250cc motorcycles, not scooters. As you say, something completely different.