Say a train is moving in the positive $x$-direction at 100 meters per second with respect to the ground frame. Now let's say someone is pushing a large box in one of the cars of that train in the negative $x$-direction and is applying sufficient force to keep the box moving at a constant 5 meters per second in reference frame of the train car.
My intuition keeps telling me that this is like any other problem where the ground frame observer would witness the force being applied over a longer distance compared to the pusher/observer in the train frame, so work done is greater in ground frame, but isn't the energy dissipated as heat independent of reference frame?
Furthermore, the ground observer would see the box moving forward at 95 meters per second as the train moves forward at 100 meters per second. Correct? The person pushing is doing work and the friction is doing equal work in the opposite direction. From the ground frame we'd see much more work done but how do we account for the dissipated energy such as heat and vibration? I feel like from the ground frame you'd see enough heat to start a fire. I hope I have articulated my confusion clearly enough.