The faster the engine runs the more combustion occurs as well which creates more heat. Energy cannot be created without creating heat. The reason the fan runs faster is because the engine is creating more heat at higher speeds and needs more air to prevent the engine from over heating and shutting down. It doesn't mean the engine is running cooler at high rpm. You are a race car guy. Your car runs around the track at a high speed and high rpm. Lots of air coming in. Is the engine cool when you pull into the pits? Farm Tractors are made to run at full throttle as well, but you still have to let them idle to cool before shutting them off (yes I know tractors have Diesel engines, but the same principles apply). I just found that by letting mine idle for a few minutes helps prevent backfire. I do agree that you should only move a hydrostatic mower at full engine throttle though.
Your logic is both right and wrong.
Yes running at full speed does generate more more heat.
However the rate that the heat is transferred to the engine rather than blown out the exhaust is directly proportional to the time the hot gasses are in contact with the cylinder / head piston & valves.
This heat transfer rate is called the R value, the said same R value that you are used to for rating insulation
And to bring it into focus, aluminium melts at 700 deg C dut your cylinder reaches 1800 deg C why does the piston not melt ? or for that matter the inside of the head ?
So the faster you get the gasses out the less heat will be transferred to the engine.
You have obviously never had much to do with old long stroke vintage engines which will happily sieze at speeds well under 1000 rpm.
It is also one of the reasons why you have more exhaust port than inlet port.
Then there is the volumetric efficiency of the fan, the higer the fan speed the more efficient the fan and the volume of air moved per revolution of the fan actually increases substantially till its viscious limit.
So at higher speeds you are getting more air per BTU and increased cooling efficiency.
Yes there is more heat being generated but it is being transferred to the engine at a decreasing rate and being removed by the air at an increasing rate.
And before some clot makes an idiot extrapolation, no, it won't eventually freeze like all physical matters there is a limit all thermal graphs are curves
And then there is the internal cooling being done by the oil and the volume efficency of the oil transfer system and residual oil to consider.
Running a Vertical shaft engine too slow will reduce the volume of oil at the top bearing because at slower spees the oil drains through the top bearing a lot faster because the gravity forcing the oil doen is not fighting against the centrifugal force trying to fling the oil out onto the bushing wall.
So funny enough the engine companies actually have it right.
And as for some idiot reason people always have to bring in comparisons between things that are totally irrelevant .
Have a good look at the NAS Car videos of drivers comming into the pits.
Do they sit there and idle for 2 minutes before thay shut down or come in at full revs and switch strait off, Do they idle in a high gear to keep to pit lane speed limits so the engine is cooled down better or come in running hard in a low gear ?
And of course all of this is totally irrelevant but resorting to irrevelevance seem to be the norm now days.