Thermostat placement can be a tricky thing, if you're suggesting Amtrak should upgrade to a thermostat in each car.
Some examples of things that don't work well that I've seen actually in place in the real world:
I've slept in a house that has multiple heating zones. The upstairs of the house is one zone, and I think there are two zones in the downstairs. Anyway, the upstairs has two bedrooms and a bathroom, and the hallway is kind of a small square that has a door on each of three sides leading to the three rooms, and stairs on the other side. The radiators for the upstairs zone are located in the bedrooms and bathroom, and the thermostat is in the hallway. The net result is that if you close all three doors (or possibly even just both bedroom doors), the thermostat tries to maintain a constant temperature in the hallway, and when it wants to raise the temperature of the hallway, it has to make the bedrooms uncomfortably hot in order to get enough heat to leak through the doors into the hallway.
I've also seen a server room that had a 3 ton air conditioner mounted in the ceiling, and a one ton spot cooler. IIRC, there was originally one rack of servers between the spot cooler and the thermostat that controls the ceiling unit. I noticed that this rack in between things had a fairly constant temperature relative to the far end of the room away from the spot cooler, and developed the hypothesis that the spot cooler was cooling the thermostat well, convincing the ceiling unit to shut off, but then the spot cooler was failing to have enough capacity to cool the far end of the room. Eventually we moved the spot cooler away from the thermostat, and the room temperature did become more stable.
It sounds like if you're proposing to just replace the control system in a sleeper car, the thermostat needs to have a single on/off output for the entire car. So where do you put the thermostat? If you put it next to a door to the outside world, chances are that a sleeper passenger staying in their room during a station stop is going to notice a temperature flucuation during the station stop that is far greater than they'll see with the current system, as the air conditioner adjusts the amount of cooling it's providing to the rooms as a side effect of trying to keep the hallway at a constant temperature.
And if you put the thermostat in a room (maybe the sleeping car attendant's room), whether that room's door is open or closed and thus is exposed to air from the hallway is likely to make a significant difference. Sleeping car passengers probably don't want to have to adjust the number of blankets they have keeping themselves warm every time the sleeping car attendant leaves his or her room in the middle of the night.
So short of dividing the sleeper car into a separate zone for each room plus a hallway zone (maybe both an upstairs hallway zone and a downstairs hallway zone on the Superliners), I don't think a thermostat would help anything.
On the Viewliners where each room has its own heating knob, I'm not sure thermostats would be a bad thing for heating.
But then the other question is how rugged the thermostats are. I think traditional thermostats have mercury switches in them, and maybe newer basic thermostats use something else. But I think with that kind of thermostat, the vibration of the train will likely cause problems, especially if you're using it to cycle an air conditioning compressor on and off, but even if you had the themostat controlling a mechanical relay that controls power to the heating coils. And in a typical residential setting, I get the impression that the fancy digital stuff is not quite as robust, even though it might be less bothered by the vibration of the train. If you want something that's not going to break if you think Amtrak is going to have trouble fixing it when it does, I'm not aware of any existing thermostat technology that I'd think would be a good idea.
One other thing I wonder about is whether there are ever problems with the side of a car closer to the sun being significantly warmer than the other side of the car.