Air Conditioner does not cool on a consistant basis.

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1999 Chevrolet Silverado, V-8 Vortec. Last year, Feb 2009, I had to have my water pump replaced. Now I'm having problems with my a/c and I wonder if it is related to the water pump replacement or the thermostat. In the morning when I drive to work my air conditioner works fine. It's cool in the morning as the engine has been off all night. In the afternoon, after the weather heats up, the air conditioner will run fine for about 10 - 15 minutes then the cold air will stop and it will quit cooling. I have to turn the a/c off for about another 10 - 15 minutes, then turn it back on to start cooling again. However, this cycle is a very repetative one. Another 2 miles down the road and the a/c will stop cooling again. Turn it off for about 2-3 miles, turn it back on, it's cool. The the cycle starts again. One added note, the deeper into summer it gets my gauge will indicate it's running hot if I stay idle for very long. Once I get moving, it will eventually go back down.