Luckily the high power level is maintained at reliably high speed [0], ensuring airflow for cooling.
Even better, aircraft by its very long-range nature will have much larger battery:engine ratio. For example this 2018 article [1] discusses airplane with 9x the Tesla's battery capacity and 3x the Tesla's engine power, in other words, its batteries would need to handle only 1/3rd electrical load as much at peak load (per unit). The lower power density[2] of the battery pack again provides for easier cooling; perhaps even passive cooling or air cooling instead of forced liquid cooling. Whereas Tesla's sustained performance is limited by battery pack thermals.
Lastly, it's worth noting the ICE aircraft engines are "overbuilt" as compared to the roadgoing ones, mostly for sake of reliability.
--
[0] aside of the engine run-up and initial acceleration, but both of those are short anyway
[1] https://news.ycombinator.com/item?id=18602771
[2] not to mix it up with energy density
Long-haul alt-energy aircraft utilise very low airspeed (low drag), extreme mass budgets (they're wonders of materials and structural engineering), and altitude profiles (potential energy0 to manage overall energy budgets and use.
While that is true of jets optimized for altitude, small piston aircraft (cessnas) do not burn nearly that much fuel on takeoff. Small aircraft can generally do a dozen or more takeoff/landing cycles on a single tank.
Range is ~615 miles at 39 mpg highway.
Passenger and cargo capacity is another 1,500 lb on top of this, give or take.
This is far lower than any conventional aircraft, though a few ultralights might compare.
The Cesna has a 140 mph cruise, a bit over double that of the Camry on highway, but that still means 20 lb at equivalent distance for the car, less than half the light plane.
Aircraft are fuel burners.
(Agreeing, just giving land-travel equivalent.)
Top Gear did an amusing test where they had a Toyota Prius drive flat out around a track, with a BMW M3 (a larger, heavier sports sedan) keeping pace with it.
Over the course of the test, the Prius returned 14.3 miles per gallon; and the BMW M3 achieved 16.1 - despite the fact the BMW has a 4 liter turbocharged, six cylinder engine vs. the Prius 1.5 liter, four cylinder.
I don't see your point however - what I'm saying is that at 130kmh (standard motorway speed in most of europe) a 70-90hp subcompact (by far the most common car in europe and the world in general) is running at above 80% max power (testified by the fact that as soon as there's a significant incline their speed will fall back to 110-120). So running long times under heavy engine load is quite normal for cars
Air resistance vs not having enough air to push.
Basically - you can design the prop for high altitude, but then takeoff is gonna not be great. You could design a variable prop system (or even have 2 different ones?) but then weight / complexity.
His plane is VTOL so the overpowered engines for supersonic will work well for liftoff.
I don't know how much weight a anti-ice/de-ice could add.
My point was only that once you think about it and redesign everything around the new constraints, you can come up with things that we don't yet think about.
A slow, economy cruise setting in a Cessna 172 is a 45% power setting - ~80 hp, and climbs will be at full power (180 hp).
On the other hand, you might only need ~20 hp to maintain 65mph on a level road in a sedan; and most people never use anything like the full power of their cars for more than seconds at a time.