In both the brush motor and the brushless, the resisitivity of copper goes down as temperature goes down:
http://en.wikipedia.org/wiki/Resistivity
this reduces the armature resistance Ra. According to Ohm's Law, a greater motor current flows at lower resistance:
Ia = Vs/Ra
The heat dissipation as power in an armature/stator coil:
Pdiss = Ia*Ia*Ra
where power is the square of current so smaller resistor can cause greater effort to dissipate power.
The temperature build-up depends on a thermal resistance that you might find in an industrial motor specification, and the power dissipation level. The insulation on the coils melts at some temperature.
Exactly how these factors add up to a thermal failure in a given system is a matter of further analysis.
Magnets can fail too due to thermal and magnetic circuit limits but I'm not prepared to describe any physics at this point.
Peak mechanical motor power does go up when motor resistance goes down, so the physics predicts an advantage, but the heat dissipation is the key to sustained advantage in most racing machines.