If you have a wall mounted thermostat just jump the to wires leading to it.
Highly unlikely it is the thermostat as all that is a simple single pole switch.
You say the AC is not getting cold. First off I am assuming the fan is running. If so and lowering the thermostat or jumping out the thermostat should cause the compressor to come on. If the compressor does not come on after a minute odds are it is bad. If it comes on and the unit is not putting out cold air the unit may have lost its charge or if you are lucky the coils may just be very dirty.
You can clean the coils by dropping the shroud and removing the hold down bolts to get access to the face of the coil. With a spray bottle of Simple Green spray the face of the coils and let it sit for a bit. Now with a spray bottle of water or better yet a weed sprayer with water, more pressure, wash down the coils.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles