a/c turns on and off

hi im having problem with my 01 xj's a/c it blows cold air when i just first started the engine and after 15 minutes or so it begins to blow warm air and it will turn back on if you wait for about 20 min......ive been adviced that my thermal cycling switch gone bad? and ive been calling auto parts stores for one and none of them carry it ....i just recharged the freon that didnt work.......pls pls help