Due to its inefficiency, the two strokes exhaust is cooled by unburned fuel and oil.

Why do 2 strokes run cooler than 4 strokes?

The 2-stroke has much more cooling area because it has a much greater ability to generate heat. Even compared to modern MX bikes, the 2-stroke still has a greater ability to generate heat. It's just the 2-stroke makes more heat when going fast where the radiators are efficient about rejecting heat.

Why do 2 stroke engines have higher cooling capacity?

A 2-stroke engine has higher output power than a 4-stroke engine. These engines have lower output power than two-stroke engines. It produces more heat due to that it requires higher lubrication and cooling.