The same components as found for the DC brush motor can be found for other motor types. We only have to realize that for Brushless DC motors and AC Synchronous motors the coils are mounted on the housing. This means the thermal resistance Rcoil-housing is relatively small and excess heat can be transferred relatively easy. Therefore these motors are very robust for overheating.
In AC synchronous linear motors, the coils are mounted are part of a platform, on which the load can be attached. To get the same thermal model we consider the platform to be the housing. Depending on the type of motor the housing can have a medium thermal capacity (iron core motors) or a very small thermal capacity (ironless motors). Because the all excess heat has to be removed through the air, linear motors will heat up easily. That is why sometimes forced cooling (water) is applied.