2002 bmw 3 series intermittent ac

Cars ac will blow cold and fine for long periods and then stop for no apparent reason. After a a period of time it will turn cool again. Fan operates correctly. Just sometimes the air blows cold sometimes it blows warm even though it is always set to cold. Car shows no codes. You can hear an audible click when teh air turn cold again.

I thought i read somewhere to replace the thermostat but i fail to see how that would affect A/C. Maybe heat or the car overheating but i cannot see how that would affect blowing cold. All help is appreciated.