What causes a brushless motor to heat up?
What causes the motor to burn up is mainly current (which is proportional to torque in DC motors). Running at higher RPMs means higher frequency currents running through the motor since the currents change direction more frequently through the windings due to commutation, and this induces eddy losses in the core which causes additional heating but this is normally small.
That's why high revving motors can put out much more power for the same size, because it's the current (proportional to torque) which burns the motor up, not the speed. But high-revving motors put out most of their power as speed and not so much as torque. Most applications tend to require more torque so you tend to need a gearbox to turn all that excess speed into necessary torque. Rewinding the motor to a lower kV also as a similar effect as a reduction gearbox. Of course, excessive speed will throw bearings and magnets and excessive voltage will fry the winding insulation.
A motor outputting a CONSTANT 1N-m of torque and spinning at 2000RPM will be double the output power, but have approximately the same heating as the same motor outputting a CONSTANT 1N-m of torque spinning at 1000RPM. I emphasize constant because changes in velocity will causes current spikes similar to a motor momentarily stalling and these currents will be higher with the higher RPM case since the running voltage will be higher, which means a larger difference between the supply voltage and BEMF whenever a dynamic speed change occurs. Also remember that a propeller's torque increases with speed.
You use a gearbox to make the propeller appear to the motor as a smaller (aka, higher RPM, lower torque) propeller which allows the motor to run cooler since what causes most of the heating is torque = current, not speed, while still maintaining the same power output. Rewinding the motor to a lower kV has a similar effect since it allows the motor to produce more torque with the same current, at the expense of lower RPM for the same voltage.
Generally, you cannot do what you are suggesting without a gearbox or without rewinding the motor for lower kV. On an airplane where propeller torque is increases with speed, increasing voltage increases RPM which increases torque which increases current which increases both heating and power output. But a gear box enables you to fiddle with that while keeping power output at the propeller the same by not having it spin any faster when more voltage applied to the motor, thus reducing torque on the motor and running at increased motor RPM instead.
You might potentially get away doing it with no gearbox (or without messing around with the ratios on your current gearbox) on something where the load torque is rather independent of the RPM, like a wheeled vehicle, as long as you accelerated slowly and smoothly to get around the dynamic speed change issue mentioned earlier.
You also cannot really run at a higher voltage and dial down the throttle. There are other factors at play. A motor running at 24V at 100% throttle is not the same as a motor running at 48V at 50% throttle. In a perfect world it does, but we don't live in one.