Yes, you will need to remove the complete burner assembly for easier access to the thermocouple. please follow the step by step instructions. NOTE: The gas tubing has left hand threads.
A common symptom of a faulty thermocouple is the pilot light will not stay lit. Check that the thermocouple connection to the gas valve is tight and the other end of the thermocouple is properly positioned in or near the pilot light flame. If it appears properly installed then it may need to be replaced.
Turn off the gas supply to water heater.
Remove outer and inner doors.
Disconnect the burner assembly from the gas control by loosening the pilot tube, supply tube and thermocouple connections.
Remove burner assembly from the combustion chamber.
Remove the old thermocouple from the bracket. It may be held in place with tension or a screw. Loosen the screw, if any, and pull firmly and twist the thermocouple from the bracket.
Install the new thermocouple. Position the thermocouple tip so that the pilot flame heats the top 1/2 inch of the tip.
Replace burner assembly in combustion chamber.
Tighten the main burner supply tube, pilot supply tube and thermocouple connection to the gas control valve. Turn the thermocouple no more than one quarter turn beyond hand tight.
Turn on the gas supply
Check main supply tube and pilot supply tube at the gas control valve for gas leaks with a soap and water solution. Bubbles indicate a leak. Tighten all connections if a leak is found.
Light the pilot light.
Check that 1/2 inch of the thermocouple tip is positioned in the flame.
Replace inner and outer doors.
Replacing the thermocouple should restore power to operate the gas valve and keep the flame going. If the problem continues, the problem may be with the gas valve itself. If the gas valve fails, due to its high cost, it may make sense to replace the entire water heater, especially with older models.
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services
SAFETY NOTICE: Be sure to disconnect power to the appliance before performing any repairs. If you are not comfortable with doing any voltage checks that might be recommended, please contact your local service provider for repairs. Be aware that there could be sharp edges inside the appliance that could cause cuts or other injuries to yourself or others.