The gas water heater thermostat is part of the gas valve

The gas water heater thermostat is part of the gas valve. The thermostat cannot be replaced independently from the Gas Valve For Water Heater. In addition, there is no practical way to test it. You can replace the Gas valve supplier, although, unless your water heater is not working at all this should not be needed.
Are you convinced that the thermostat is not working properly? You could test the temperature of the water coming out of the tank. The reccommended temperature is 120 degrees.

You can make adjustments to compensate, if you find that the temperature is too low. Be very careful about raising the temperature above 120 degrees. Burns and scalding can occur.

Problems of Water Heater Gas Valve

A water heater gas valve cannot be repaired. If a valve malfunctions it must be replaced.

If the pilot button does not pop-up when you release it, cut the gas off and replace the gas valve.If the control knob will not turn don't force it. Replace the Gas Top Burner Valve .If the high limit has shut the gas valve down the valve must be replaced. It will not reset itself. This will only happen if the thermostat has malfunctioned and the water reaches extreme temperatures, in which case the Gas Valve would need to be replaced anyway.

The pilot valve and the compound valve

The pilot valve is a small, ball-type, spring-loaded check valve, which connects the top of the passage from the valve chamber with the passage through the main valve stem. The pilot valve is the control unit of the relief valve because the pressure at which the relief valve will open depends on the tension of the pilot valve spring. The pilot valve spring tension is adjusted by turning the adjusting screw so that the ball will unseat when system pressure reaches the preset limit.

Fluid at line pressure flows through the narrow piston passage to fill the chamber. Because the line and the chamber are connected, the pressure in both are equal. The top and bottom of the main piston have equal areas; therefore, the hydraulic forces acting upward and downward are equal, and there is no tendency for the piston to move in either direction. The only other force acting on the main valve is that of the main Gas Valve spring, which holds it closed.

When the pressure in the high-pressure line increases to the point at which the pilot valve is set, the ball unseats. This opens the valve chamber through the valve stem passage to the low-pressure return line. Fluid immediately begins to flow out of the chamber, much faster than it can flow through the narrow piston passage. As a result the chamber pressure immediately drops, and the gas stoves freestanding begins to close again, restricting the outward flow of fluid. Chamber pressure therefore increases, the valve opens, and the cycle repeats.

So far, the only part of the valve that has moved appreciably is the pilot, which functions just like any other simple spring-loaded relief valve. Because of the small size of the piston passage, there is a severe limit on the amount of overpressure protection the pilot can provide the system. All the pilot valve can do is limit fluid pressure in the valve chamber above the main piston to a preset maximum pressure, by allowing excess fluid to flow through the piston passage, through the stem passage, and into the return line. When pressure in the system increases to a value that is above the flow capacity of the pilot valve, the main valve opens, permitting excess fluid to flow directly to the return line. This is accomplished in the following manner.

As system pressure increases, the upward force on the main piston overcomes the downward force, which consists of the tension of the main piston spring and the pressure of the fluid in the valve chamber. The piston then rises, unseating the stem, and allows the fluid to flow from the system pressure line directly into the return line. This causes system pressure to decrease rapidly, since the main valve is designed to handle the complete output of the pump. When the pressure returns to normal, the pilot spring forces the ball onto the seat. Pressures are equal above and below the main piston, and the main spring forces the valve to seat.

As you can see, the compound valve over-comes the greatest limitation of a simple relief valve by limiting the flow through the pilot valve to the quantity it can satisfactorily handle. This limits the pressure above the main valve and enables the main line pressure to open the main valve. In this way, the system is relieved when an overload exists.

Smaller relief valves are similar to relief valves in design and operation

Smaller relief valves, similar in design and operation to the main system relief valve, are often used in isolated parts of the system where a check valve or Gas Top Burner Valve prevents pressure from being relieved through the main system relief valve and where pressures must be relieved at a set point lower than that provided by the main system relief. These small relief valves are also used to relieve pressures caused by thermal expansion (see glossary) of the fluids. Figure 6-11 shows a typical relief valve. System pressure simply acts under the valve disk at the inlet to the valve. When the system pressure exceeds the force exerted by the valve spring, the valve disk lifts off of its seat, allowing some of the system fluid to escape through the valve outlet until the system pressure is reduced to just below the relief set point of the gas stove valves.

Water Heater Gas Valve-How to Work

The gas valve controls the pilot light and the water temperature.
When lighting the pilot of gas stove valve, the button on the valve is pressed and a small amount of gas is sent to the pilot head. After the pilot is lit it will heat the thermocouple.
The thermocouple will send a small electrical current to the control valve. When the gas valve receives the current, an electromagnet will open a safety valve and allow gas to continue to flow to the pilot. At this point the pilot button can be released. The pilot will continue to burn.

There are two probes protruding out of the back of the valve.
The shorter probe is a safety device. If the thermostat malfunctions and water continues to heat the probe will interrupt the gas flow. It is called a high limit probe.

The longer probe is the temperature probe. As the water heats and cools a rod inside the probe pushes a lever in the gas stove safety valve and cuts the gas on and off according the the temperature setting.

Safety Advice of Water Heater Gas Valve

Gas can be extremely dangerous to work with if you're not sure about what your doing. At the same time, gas safety valves is safe to work with if you do know what your doing and follow all safety rules. If you do not feel 100 percent confident and understand safety precautions, please call someone to help you.
Always check gas lines for leaks after reinstalling them. Soap and water works well. Spray gas safety valve on all connections and watch for tiny bubbles to form. If you do see bubbles tighten the connection and test again.
Before lighting a pilot stand near the water heater to see if you can smell gas. Kneel near the gas valve and smell for gas.

If you smell gas, find the leak and repair it or call your gas supplier. Don't try to light the pilot.
Never fire a water heater burner with the access panels off.
Never tap or hammer on a water heater gas valve.