I live in a rental house and the thermostat is acting up. It worked perfectly in the summer for air conditioning, but the heat part of it is what acts up. When we turn thr heat on, it doesn't turn off when it reaches the set temperature. What causes this?

Probably wired incorrectly. If possible, post a pic of the wiring connections at the thermostat. If the heating circuit is connected to the "B" terminal instead of the "W" terminal, the heat will run any time the system selector switch is set to heat, regardless of temperature setpoint.

If at one time the tstat worked fine then its probably bad. If this is a new tstat and never tested in heat mode then I'd say its wired wrong.