Why do brushless motors heat up?
The motor is converting electrical energy in mechanical energy, and unfortunately all energy conversions lose some energy to heat. This site states the cause of the heat losses as:


Friction losses due to bearings etc.
Windage losses due to air resistance.
Iron losses caused by magnetic paths of the motor (hysteresis losses and eddy current losses).
Ohmic losses from current flow.
Stray losses: other