97 century A/C coming on and off?

[rhvcjack]

When i have the A/C running, after a short time, it starts to blow ambient, muggy outside air. Then after a little while, it will start blowing cold air again. It seems to cut off when i lift off the gas, or i am at idle. When i accelerate, it comes back to cold air again. I've read back through a lot of posts looking for this problem, but havent found much. I did find a thread which mentioned an outside air temperature sensor as a possible cause, but i'm not sure if my car has this sensor. I don't have an indicator inside my car telling me the temperature outside. Even though i don't have a display for outside and inside temperatures, does my car still have them? And could they be the cause of my problems? My other thought, since it seems to vary with engine speed, is the compressor. But, i'm no A/C technician, so i will humbly defer to all of you for your valued knowledge and assistance in this matter.
Thanks,
Ray