Crack open your gas cap. See if it makes the engine run proper after say 1-2 minutes. After 1-2, the fuel bowl will get low and make the engine stumble. If your vent in the cap is bad, it will cause this.It stops the fuel flow to the carb.
Bet someone just threw on some carb they had sitting in the garage just to try it out??
If the engine has a small oil leak or someone misses the funnel when changing the oil, some how oil will find its way to the top of the engine block. Then when you dirt mow, makes a dirt/oil/grass/bugs dam on top of the cooling fins. I've seen birds and mice nests and of course there's always a ton of oil up there. If you neglect this step, you will get valve seats popping out and such. Burning oil from the bore getting out of round and so on. Internal engine issues from improper/lack of maintenance.
Air cooled engines like these got hot in less than one minute or shortly after. Not like a car engine with water that takes minutes to heat up. Surface dirt like you see on your mower shouldn't cause an over heat. Unless you get oil and grass up there with it. Keep the sucker clean. Use a blower after every mow and a dusting paint brush. Clean the air filter after every mow with your paint brush,.especially when you dirt mow. Put a small trail of grease around the air filter sealing gasket. Helps stop the dirt from getting inside the engine.
slomo