Central air-conditoner runs thru cycle, shuts past its sell-by date afterwards comes right fund on for another few minutes. What is it It cools good. It will run thru cycle, shut off and...

It cools good. It will run thru cycle, shut off and later immediately come back on and blow cool nouns for a few minutes, shut off and it may repeat this several times. Does not always do this. We installed a unusual thermostat and cleaned filter.
HVAC Tech.: yes! Even foreign thermostats can come damaged. (Most likely cause) 2.)could be wired within wrong. 3.) Intermittent short/open Thermostat to contactor/blower. get the facts on operating your A/C unit.
Make sure the heavens from the vents are not affecting the thermostat operation.
Maybe there is a problem near the thermostat.
Most electronic thermostats have a built in cycle rate of 4 times an hour and might destroy this problem.
Could be your system is over sized and is not doing a good job on removing the humidity.Cooling the atmosphere quickly but not running long enough to scrub the heavens of its moisture content.
When it's real hot out it would run longer and do a better job cooling and dehumidifying.
Answers:    sounds like it is hitting a fault code. if its a newer model in that will be flashing lights that designate the code. take off the front panel and read up on it
could be a doomed to failure fan relay. if it just started, it wouldn t be oversized.