Air Conditioning - AC too cold

Last night I was up in the middle of the night for our baby and I noticed that the temperature in the house was cooler than normal. We typically have the setpoint at 78, but the temp was down to 72, and the central air was still pumping out cold air. The system kept running no matter where I put the setpoint, and even after setting the thermostat to 'off'. Does the stat just need to be replaced?

But you should first verify that the stat is actually keeping everything on even when stat is off. Do you have a volt meter and know how to use it?

Also, is it possible that when you turned the thermostat to off the fan was set to "on" rather than "auto"?

I changed out the thermostat, but the system is still not working correctly. Even when the temperature is below the setpoint (5 degrees or more) the blower will run all night when it is set to auto. I'm assuming theres something wrong with a blower relay? Is this something a professional needs to diagnose/fix?
thanks

Is the outdoor unit running as well when the temps is below set point, or just the indoor blower?

What brand/model of t-stat did you get?

its just the blower running. I've noticed that if I shut the breakers off for the unit, it will run correctly for a few days before reverting back to the blower running continuosly. it is a ritetemp stat, purchased at homedepot. said it worked for all central air systems. It is not hooked up to our heating system as we have hot water baseboard, not forced air.

Sounds like the symptom of what can happen when contact points are involved, and you can sometimes get a flash of spark from a poor electrical contact that then causes the contacts to weld togeher sometimes, and not release. Yet sometimes might. Water well pressure switch points do that, appliance timers do that, and any relay with contacts in it could do that.

I'm not sure, with thermostat design, if it is possible to have contacts release, that send low volt power to the outside unit, while yet not releasing contacts to the indoor blower. I have never gotten a call for this, but can't say it is impossible or not with every design fo thermostat. Other than that, I'd be looking at relays, as mentioned.

Probably a relay on the board (that is sticking sometimes) that governs your blower motor, and maybe even is one that is adjustable for time? If you have such a thing, try adjusting the time a little, as often by fiddling with adjustments, you can change the geometry with contacts, like on water heater thermostats, to cause the thing to work right again, for a long time without further problems.

I think there something sticking on the board/relay. If it happens again, i'd call for service.