Why wouldn't you expect the FETs to run hotter ..... under the PWM
1) when the FET / motor is off it should be generating no heat because there is no current through it.
2) when the FET / motor is on it will be generating heat because of the current flowing through the on resistance of the FET.
3) When the FET is being turned on / off at say a 50% duty cycle then the heat situation alternates between 1) and 2) and so it runs cooler than 2).
Why wouldn't you expect the FETs to run hotter (less efficiently) under ...... linear mode
Now here you are making a definition of less efficiently that is not valid. In the linear mode it is designed to burn off the excess power and that is what it is doing very efficiently. There is no change in efficiency of the FET, the lack of efficiency is due to the design decision to have the FET burn off excess power.