A/C problems cold than warm Compressor is running

The A/C works after the car has sat & cooled down. After the car gets up to normal running temperature. When I turn the car off briefly when I start it back up a/c blows warm air. But the compressor is running does this mean I’m low on coolant because I tested it with gauge that came with the last coolant. I bought a few years ago for a different car, but that wasn’t real. I don’t believe that was working correctly.

I don’t want to spend $40-60 on a new gauge & a can of refrigerant if that’s not the problem.

Any advice?