I have a 21 year old Carrier single phase a/c unit. I did the kick start test on the fan blade and it began to spin as if there was nothing wrong. About 20 minutes later the fan stopped on its own. I pulled the cover off and checked for voltage at all of the terminals and all seemed to be O.K. Once again I manually started the fan blade and noticed the voltage at the brown wire at the capacitor went from 120V to 165V as the motor developed full speed. The capacitor is appearently the original and doesn't look bad. The fan motor was extremely hot and so was the start thermistor. I assumed the motor was bad and replaced it. I now can energize the system and the fan will start on its own. Eveything was working fine then, once again the fan stopped. My two question are, is this the capacitor or the start thermistor and which way should the air flow in an exterior a/c unit.

Hope someone can help, Thanks

Did you replace the capacitor with the motor? The capacitor is a cheap item and may not be the proper size for a different motor (the proper size is stated on the motor)and it sounds as though the capacitor was bad from what you say.If you look at the fan blade you will see that the blades are bent like scoops and as the motor rotates it must scoop the air and throw it either up or down, if you look down on the fan blade and the scoops are facing up, the bottom of the blade on the left is facing towards you it should rotate CCW, if it is facing away from you it is CW (clock wise) rotation.
The fan should pull the air through the coil.