1999 F-150 AC starts to blow hot air when you acclerate

Hey, I have a 1999 F-150. It is the 4.6 V-8 with an atuo transmission. I am having problems with my air conditioner. When you first crank the truck up the air blows COLD. When you accelerate a little hard to starts blowing HOT air. I hear what sounds like the diverter door moving. If you crank the truck up and leave the truck in park and rev the engine it DOES NOT start blowing hot air. I checked for vacuum leaks but I did not find any. What does it sound like may be the cause of the problem?