[BrianG]

From an amp-draw perspective, what Squee said may not make much sense, but you have to remember that these BL motors are AC motors. As such, there are other factors like inductive reactance, power factor, etc that come into play that can make a large difference in current draw and temperature.

When motor current draw is high, but there is little motor heat, this means the motor is presenting a highly inductive load, which tends to be hard on the driving circuitry (ESC) and heats it up.

When the motor is hot, the motor is presenting more of a resistive load to the controller due to the frequency of the AC signal and loading of the motor. Resistive loads are the easiest to drive and therefore the ESC is cooler (still depends on the current draw though somewhat).

If the motor and ESC are about equal in temperature, then there is a good balance of resistance and inductive reactance, and power factor is closest to the ideal value of "1".

It's the resistive component of the motors windings that create the heat (and any other mechanical/electrical losses). On an ESC, the majority of the heat is generated by the rise time of the square wave pulses across the FETS devices. During this time, the voltage is neither on or off so there is a voltage drop AND current draw - hence the heat. When FETs are off, there is a voltage drop but no current draw so no heat. When the FETs are fully on, there is is current, but no voltage drop, so no heat there either.

This is oversimplification because there is a LOT of thought that goes into the design of an ESC and its feedback/speed sensing circuitry.

BTW: Ask any master electrician and they can tell you all about BL motors but they know them as "squirrel cage" motors and have been around for a LONG time. AC drive circuits are not new either, but their use in R/C is relatively new in comparison because we take DC and create PWM AC to drive the motor. ANY 3-phase AC motor is really a brushless motor.