I woul highly recomend it but you dont need to
No You don't Need to change the water pump But you should change it and the thermostat if radiator was full of sludge. if not then no to both.
To replace the thermostat on a 91 Cavalier you need to drain the radiator. Remove the top radiator hose and water inlet. Remove the thermostat from under the inlet. Install the new thermostat and reinstall the inlet and hose. Fill the radiator with fresh antifreeze.
To change that thermostat you need to follow the top radiator hose to the motor from the radiator. It will lead to the thermostat housing on the block. The housing will be anchored with (2) bolts to the block (I think). Take the housing off and the thermostat is housed inside.you will have to replace it with a manufactured suggested thermo(probably 180* or 200 degree thermo).
Changing a thermostat in a 1997 Dodge Ram 318 is very simple to do. First the radiator hose will need to be removed from the thermostat. After the hose is removed, loosen the nuts that are holding the thermostat in place. Then the thermostat will need to be pulled out using just the hands. Then replace with a new thermostat.
You may need to replace the radiator thermostat and gasket.
You need only to drain off a couple quarts of coolant to change the thermostat.
The first step in how one can replace a thermostat in a 2001 Cadillac DeVille is to remove the housing which surrounds the old thermostat. The radiator hose will need to be removed and drained and then the thermostat can be removed. Remove the old thermostat gasket and then insert the new thermostat as well as the new gasket. Attach the radiator hose and place the drained fluid back into the radiator filler cap.
To change the thermostat, you first need to get a new one. Then you can take it out and replace with the new one.
The thermostat is located in the upper radiator hose. The radiator hose will need to be removed to get to the thermostat.
First locate the lower radiator hose, that hose should lead you to the thermostat housing (just behind the motor and to the left). This hose should be the same size as the top radiator hose. Second you move the clamp (pliers will work) down the hose away from the thermostat housing, then loosen that hose from the thermostat housing. Third you take of the 2 Bolts off from the thermostat housing, they should be 10mm. Remove the thermostat. When you replace the thermostat you may also need to replace the gasket. Simply put the bolts back in and tighten them, then reattach the lower radiator hose and move the clamp back to its original position. Note: The top radiator hose does NOT lead you to the thermostat housing!
Your thermostat is stuck closed. you will need to replace it. The thermostat controls the circulation through the radiator - when the engine heats up the thermostat is meant to switch circulation from just-engine to engine+radiator. Sounds like this isn't happening.
You need to replace the thermostat and flush the system of crud.