>> holding high horsepower output levels for a long time, an internal combustion engine will overheat quickly.
Every racecar in every 24-hour race. Every large boat/ship that runs at full throttle 24/7. Every large truck pulling a load up a hill. Every diesel generator that runs at full load for weeks. Modern IC engines can run flat-out for considerable periods of time. Counterintuitively, in many ways running at high power settings is easier on an IC engine than at lower fuel-efficient setting. Some pressures between parts are lower at higher RPMs. Total power/RPM is higher, but the energy involved in each rotation of a part is generally less. Oil moves more efficiently and doesn't get squeezed out as parts push against each other. And the ignition inside the cylinder is richer (ie cooler) when optimized for power rather than efficiency. Talk to anyone riding a Japanese sportbike. Those engines are far happier running flat-out on the track than sitting at idle in traffic.
No. Flat-out means at full RPM, which is not a thermal decision. It is a limit based on cylinder size and flame speed. Any higher and the fire is still burning when the exhaust valve opens. That is why engines with big/wide cylinders cannot turn as quickly. This is why a large ship with 2-foot wide cylinders might max out at 100rpm while a sportbike with 1-inch cylinders might at 16,000rpm. The capacity of the cooling system is a different issue.
Because of the physics of air movement, sitting at idle is very hard on a car engine. Idle means no speed and air has to be forced across the radiator. Flat-out would mean at least some forward movement and lots of air across the radiators. Any radiator system meant to survived idle while stopped will handle flat-out at speed indefinitely. Those Japanese sportbikes racing around the track are not overheating, but they might if asked to idle at the start line for too long.
Where I am, it is normal to see cars/trucks with carboard across their fronts to reduce airflow. In winter there is too much cooling and engines have trouble getting up to temperature at any forward speed. This is a big issue if you are relying on the engine to warm up and de-fog your windscreen (hybrids).
>> Flat-out means at full RPM, which is not a thermal decision. It is a limit based on cylinder size and flame speed. Any higher and the fire is still burning when the exhaust valve opens.
Partially -with some engines, the limit is valve float, or cam shape (which is why electronically operated valves are becoming a thing), with some it is thermal.
With pro-level drag race cars, producing 7000+ Hp / 5+MW, some of the more key considerations are how much fuel can be pumped into the cylinders. But they turn over only something like 900 revolutions each race run and need to be torn down between each run.
The point is that ICE engine design is a massive balancing act between inertia of parts, internal friction, strength of parts, fuel, and thermal. Thermal may not be the main driver of every engine design, but if you claim thermal is irrelevant and not a limiting factor, you're just plain wrong. In many types of road races from F1 to Le Mans, merely picking up a small sheet of plastic or paper on the radiator intake will be a cause to pit almost immediately because the thermal management is designed to handle the requirements.
Every racecar in every 24-hour race. Every large boat/ship that runs at full throttle 24/7. Every large truck pulling a load up a hill. Every diesel generator that runs at full load for weeks. Modern IC engines can run flat-out for considerable periods of time. Counterintuitively, in many ways running at high power settings is easier on an IC engine than at lower fuel-efficient setting. Some pressures between parts are lower at higher RPMs. Total power/RPM is higher, but the energy involved in each rotation of a part is generally less. Oil moves more efficiently and doesn't get squeezed out as parts push against each other. And the ignition inside the cylinder is richer (ie cooler) when optimized for power rather than efficiency. Talk to anyone riding a Japanese sportbike. Those engines are far happier running flat-out on the track than sitting at idle in traffic.