Blows cold air for a minute, then stops blowing, but can still hear fan.

Sounds like a loose wire in the fan circuit

I think you have a "variable speed resistor" problem, it's overheating. It's an electronic device usually located near or attached to the AC motor blower that controls the fan speed. This is a common problem with aging AC blowers with electronic controls.

Are you RECIRCULATING?

I recharge unit for your ac

your auxillary fan is not working. this fan is responsible for cooling the freon that is being circulated in your cooling system... check if there are any loose wires in front of the engine bay.

the auxillary fan is located right beside your radiator fan.

replace fan speed resistor block if this only happens on lower fan settings if it happens on high fan speed also, replace blower fan

YOU NEED A NEW FAN UNDER RT SIDE PASSENGERS FEET ABOUT 80 DOLLARS AND AN HOUR LABOR

plus one on the cooling fan problem. if it was low on charge then as you slow down, condensor temps and line prressures would raise therefore it would cool at low speed and and not when moving since the incoming air would drop system temp,reducing line pressure and then cusing compressor to cycle. the auxillary cooling fans must be on whenever a/c is on, if not, thats your problem. get this taken care of because if you get stuck in traffic, your engine will overheat also if fans are not running

Sounds like a compressor problem.

If the A/C knob is not set to 0 at the time ignition was off, the fan could run for a little and then off itself.