BLDC motor shaft getting hot
A BLDC has a rotor with a permanent magnet. The induction motor (IM) has a squirrel cage and the rotor flux is due to induced current in the cage. In the IM most heat is produced in rotor, then transferred to the stator and through a shaft. When the IM is hot when you touch the outer stator casing, it means that the rotor is glowing red.
A BLDC is a different since the magnetic field as seen from rotor is DC, so no eddy currents are present that can heat the rotor. All the heat produced in BLDC is due to stator resistance and stator eddy currents, therefore when you touch the stator outer casing you have touched the hottest point. The heat is transferred to the rotor through the air gap (in the reverse direction as in IM).
To conclude, in the BLDC the stator shall be hotter than the shaft unless the heat is produced due to friction of the shaft - shaft bearings, load bearings, ... or transferred from the load.