First of all, to check the thermostat for a cooling system problem, start by inspecting the coolant level, drive belt tension, and temperature gauge or light operation. If the thermostat is stuck open, replace the thermostat. If the engine runs hot and the lower radiator hose is not hot, the thermostat is stuck closed, impeding coolant from flowing into the radiator, the thermostat should be replaced. Then, to remove the thermostat, begin by disconnecting the negative cable and draining the coolant, remove the engine drive belt and the alternator, then detach the thermostat housing from the engine. Also, the radiator hose can remain attached unless the housing needs replacement. Next, remove the thermostat, and clean the sealing surfaces thoroughly. Place a new gasket evenly onto the thermostat, ensuring it fits properly all the way around, install the thermostat along with the housing, and secure the housing fasteners to the proper torque. The installation is the reverse order of removal. Finally, refill the cooling system, start the engine, and check for any leaks or irregularities.