Turn off the gas supply leading to the water heater.
Press the lock tab under the gas control knob on the front of the Kenmore water heater. Turn the gas control knob to "Off."
Loosen the screws holding the access door in place. Remove the door.
Disconnect the thermocouple connections from the gas control assembly with the wrench. Disconnect the pilot supply tube with the wrench.
Lift the burner assembly out of the Kenmore water heater.
Remove the screw holding the thermocouple to the burner assembly. Position the new thermocouple into the assembly. Install the screw that holds it in place.
Replace the burner assembly into the water heater. Connect the thermocouple and pilot supply tube connections.
Replace the access door. Tighten the screws that hold the door in place. Turn the gas supply on.