I replace my thermostat thinking this is the problem. However, my furnace will not stop even when the temperature has been reached or even after I turn off my furnace. The same is true for my air conditioning. What do I do?

so you need to check the thermostat wiring it seems

Thermostat may be bad or element grounded out.

That's how it should work .Your furnace will cycle on and off to reach set point .
You don't have to troubleshoot the thermostat. The reason why your furnace cycle is once the heat exchanger get to a certain temperature the board will shut it off, fan would still work to cool heat exchanger down then once cool down furnace will fire up again .

Hi Demetrio
Furnaces turn on and off based on what they're told by your thermostat. The thermostat, in turn, will control the furnace based on:

1. The temperature AT the thermostat.
2. What the internal heat sensor thinks the temperature of the air is.

So, if your idea of 68 degrees is what the thermostat thinks is 71 degrees (thermostat reads three degrees high), then when the air by the thermostat gets to about 65 degrees (by your account), it'll think it's 68 degrees and shut the furnace off.

Also, if the thermostat is, say, near a source of local heat, like a lamp, a big piece of electronics, a fireplace, or that place that you habitually set down your coffee, then the air right next to the thermostat may be warmer than the rest of the room, and fool it into thinking it's at it's target.

The sensor is usually inside the housing for the thermostat. If it hasn't been dusted in a while, then it can be hard for air to get inside to affect the sensor, though this would generally cause it to lag on readouts and run the temperature higher than you wanted.

If you have a digital readout, and the system is saying , hey, target is 68, and the readout gets to 66 and the system cuts off the furnace.... my only other guess is that the unit may have features that are trying to prevent overshoot - i.e. by the time the temp at the thermostat actually gets to 68, most of the room is more like 73. That'd depend on your particular thermostat. At that point, you may want to call customer service with the manufacturer and tell them the issue. There may be ways to adjust the unit to get behavior closer to what you seek.

Good Luck!

DH

Some thermostats allow you to change the differential value - that is how far below the heating (or above the cooling) set point before calling for heat (or cooling in the case of air conditioning). The built in 1 degree differential setting provides the most even temperature in the space at the expense of more frequent furnace firing and stopping. Many people prefer this mode as opposed to allowing wider swings in temperature for less frequent furnace firing and stopping. If you wish to change this setting, you'll need to replace the thermostat as it is not user adjustable in this model.

Does the furnace stays off?.
Furnace are ment to cycle on and off because of limits .If you set to 70 furnace would cycle several times before reaching that temperature.
Just make sure your filters are clean and you got proper return air flow because lack of air flow will cause furnace to shut off sooner than normal

yes, sounds like a stuck relay. RAY YOU ARE A GENIUS!!!

If you need further help, reach me via phone at https://www.6ya.com/expert/thomas_092728000e6acb79

Sounds like the anticipator on the thermostat is faulty.
Try replacing the thermostat.

try running viniger through it , clean or replace filter , if filter was real dirty you may want to have your evap coil cleaned

first off buy yourself a honeywell stat, in my personal opinion lux stats are garbage, I have run into so many that are bad stats !!! but as far as your fan not shuting down, sounds to me like your fan center on your circuit board is bad and will not shut down the fan when needed, you will have to replace the circuit board, as the fan center is a part of the whole of the circuit board, hope that helps