Sounds like the thermostat is wired wrong. Like it is backward. Did it ever work right?
I am not a repair person in the least. Our problem is usually short cycling which is often caused by vents being blocked.
Do You have a HVAC Unit or a Heat Pump ?
Make sure that the Thermostat Unit is LEVEL. (If it is an older model with the Mercury Bulb) if it’s a newer version then it’s probably a Factory Defect and needs to be replaced.