Automatic transmissions have thermostats and others don't?

Not a thermostat, but a temperature sensor. Most cars use the engine's coolant temperature sensor. The transmission will always shift through first, second, and third gears when cold but it may not go into overdrive until the engine warms up. To do so puts more load on the engine and since it's turning slower, it pumps less oil and since the transmission oil is cold it's relatively thick, so it won't circulate as freely to important places. Some transmissions have a temperature-controlled valve to stop transmission fluid from circulating through the cooling tank inside the radiator until it warms up. That helps the fluid get warmed up faster, then the transmission will be allowed to shift into overdrive.

Just to add this one toyota does that for emissions reasons so the engine warms up quicker. Its there way to meet emissions and keep the epa happy.