Average thermal conductivity (?)
Sorry - I may have got the wrong end of the stick here. You want to calculate how hot the motor will get. It's an electric model of a thermal system - not specifically an electric motor.
It looks like you have a power source (hot wires) and a number of series thermal resistive elements with a radiative element, finally.
Thinking aloud, as it were . . . .That, at its simplest, would be a current source in series with two series electrical resistances. This would represent the thermal power dissipated internally (a fixed amount, hence the current source), a resistor for the conduction path and a resistor representing the radiative path - assuming a sink at 300K. At equilibrium, the coil temperature and the motor surface temperature would correspond to the voltages at the current source terminal and the junction of the two resistors. The 'radiation' resistor would be non-linear and would follow the Stefan Boltzman law (4th power of the temperature difference).