I had a Corvair 140 that would push past 300 F on a hot day, but it was designed to do so. I think it was pushing the limits of what you could do with an air cooled motor. It had a magnesium fan that forced air around the cylinders that were enclosed in a chamber, and further more there were baffles to direct cooling air to hot spots. The chambers had doors that opened to exhaust the heated air, and these doors were controlled by thermostats that held the doors closed until the engine warmed up. The air that came out of these exhaust vents could be dangerously hot. In the winter time this heated air was forced up into the passenger compartment for heat. This was different than the Volkswagen/Porsche method that used a heat exchanger on the exhaust pipes. That system was dangerous because when the heat exchanger rusted through the carbon monoxide in the exhaust killed the car's occupants. Yikes.
If the Corvair broke the fan belt or tossed it, it didn't take but just a few seconds for the engine to overheat and sometimes lock up. There was also a sophisticated oil cooler built into all of that that helped cooling.
You rarely see Corvairs today, but some of them made some serious horsepower. There was even a turbo 180 Corsa that is highly sought after, and the 140's like I had would eat many a muscle car back in the day. People that own LBC's (Little British Cars) hate them as they are the Corvair's favorite food group. Quite a few Corvairs had air conditioning, they were so light that power steering wasn't even offered.
A silly side note... because of Ralph Nader's claims of safety the US Gov't actually had the car tested and it is the only car to this day that is certified safe by the Congress Of the United States. I know, your aunt was decapitated by the engine when it flew out of the car while going to the grocery store...
Anyway... back to the air cooled thing, two strokes have a real problem keeping things cool if they are air cooled. Suzuki used water cooling on the GT750's back in 1972. Many H1's and H2's seized up the center cylinder because they couldn't cope. With today's emissions laws it would have to be water cooled, the combustion chamber temps would be way too high and you would be forming those dirty little nitrous oxides. Even Bridgestone's little 50cc racers appeared to be water cooled. There is no real way to oil cool them....