What is that little TUBE coming from the thermostat?
That is a Copper tube filled with Freon that sticks into the Evaporator. coil and senses the temperature. At a predetermined temp., it opens the circuit to the Clutch which allows the temp to rise to another predetermined temp (usually +8 or 10 degrees) then it closes the circuit again. This probe must have good contact with the fins of the coil or it will allow the coil to freeze up and that is not good even if it sounds good. If the coil freezes, the air must go around it and the air comes out warm instead of cold. So if you notice that your a/c works at low speed (car speed) and then quits cooling after a half hour or so, check this . Handle the probe very gently and polish the end with crocus cloth before inserting into a new location in the coil if it was loose. The probe should go in about 4″ and at an angle to get between the coils.