Sound like a Thermostat or furnace/AC problem?
Within the last few weeks, since it's gotten warm enough outside to start running the AC occassionally I've notice some strange things going on with my HVAC system. I live near Atlanta, and we get some pretty wild temperature ranges this time of year here. Can be frost on the ground in the morning and 85 degrees by mid-afternoon. Anyway, when I switch my thermostat to AC the thermostat will click, I'll hear the outside unit kick on and start to run and then the thermostat will click and it will promptly shut off. It will kick on again a few minutes later and do the same thing. Then, maybe 15-20 minutes later it will kick on and stay on and complete it's cycle with the blower kicking on and running normal. I'm not sure if it does this every time it needs to cycle as I'm not as aware of the problem later. The heat will do the same thing if I switch it on. The thermostat will click, I'll hear the exhaust fan start (it's a gas "Comfort Maker" unit if that matters), I'll hear the auto-igniter start, then I'll hear the burners light and run, then the thermostat will click and it'll all shut off. It will then repeat the process with it allowing the burners to fire longer each time 5 or 6 times until it finally stays running and cycles like normal. When the next cycle starts it may or may not go through all that again. thermostat is a Robertshaw model 9600