Understanding a cooling system is key to effective diagnosis of system issues. The purpose of the thermostat is to allow the engine operating temperature to be more controlled. With today's emissions requirements, coupled with tight tolerances that must be maintained to avoid friction-induced damage to key engine components, the temperature range for an engine is pretty narrow.
The thermostat is a device that alters the flow rate of coolant through the radiator, depending upon the temperature of the coolant. It opens at a certain temperature (195°F for the stock TJ thermostat). This means that if your Jeep has cooled down to ambient temperature, the thermostat is initially closed. When it is closed, the coolant does not flow through the radiator so that the engine can get up to operating temperature as quickly as possible.
Once the engine gets up to the thermostat opening temperature, it opens and allows coolant to start flowing through the radiator. If ambient temperature is low (cold winter day), the thermostat may immediately start to close because the radiator is very efficient in the winter. This opening and closing may happen quite frequently in cold weather, but if it's summer, the thermostat will open initially, and stay open until you shut the Jeep off and it cools down.
Now, if the thermostat sticks open, and it's a slightly cold day, at low vehicle speeds, the radiator may not cool enough to drop the temperature. It depends upon the ambient temperature and the cooling efficiency of your system. However, at higher speeds, the efficiency increases, and now the radiator cools too well, dropping the temperature of the coolant. Since the thermostat is stuck open, the coolant temperature stays low until you slow down, reducing the radiator's ability to cool and bringing the coolant temperature back up.
In really cold weather, a thermostat stuck open will actually prevent the engine from ever getting up to operating temperature. And in extremely cold temperatures (-50°F, which I've experienced many times), at highway speeds, just the air flow through the grill, even with a properly-functioning thermostat, can prevent the engine from getting up to operating temperature. That is when you have to partially or fully block the grill off, and what those "flaps" or "curtains" you sometimes see on semi-trucks in the north country do.