Thermostat
#1

I'm having a with my heatpump unit. Thermostat set point is 69degrees and unit will keep running down to 62 degrees without shutting off. I have to shut the unit off myself to get it stop. 2 1/2 ton carrier. I have replaced thermostat with same model and still same problem
#2
although
it does sound like a tstat problem, i guess you have ruled that out with the replacement. remove all wires from the tstat, does the unit continue to run? possibly a short in the tstat wire, this would force the unit top continue to run. remove the low red low voltage wire at the unit with the tstat off, if it stops, wire is shorted. somehow the fan relay and contactor circuits are energized, interesting problem. be sure the tstat is wired correctly. may need a troubleshooter out there.
#3
Contactor
I'll bet the contactor is welded shut. on the outdoor unit. Pull the panel cover with the power off see if the contactor springs have free movement. You can push them in and out with a pencil provided it has no covering over the contactor bars.

#7
try this
get an accurate thermometer, and check temp at the tstat. you will probably find tstat is off. generally you can calibrate the thermometer on the tstat by removing cover, and adjusting the thermometer dial on the back of the cover of the tstat with a small screwdriver. also, check the spring on the bulb by cutting power, and adjusting lever to where the mercury wil be in the middle of the bulb, put cover back on and see where that puts the setpoint at room temp....compare this to the accurate thermometer you have there. kind of confusing maybe, feel free to ask any questions. i would go digital, due to accuracy and ease of use.
#9
adjustment
If you can kill it by raising the temp setting...level it first, turn on the cooling till your comfortable, then slowly raise the set point till it shuts off...and leave it alone!