Diagnostic Tree: Electric Heat Problems
Most permanent electric heaters run on 240 volt circuits, and this is what will be dealt with here. (If you know yours is for 120 volts, treat its problem as if the heater(s) were a light and the thermostat were a switch; there could even be lights and outlets on the same circuit).
Before talking about individual room heaters, a word on central electric furnace problems. Many furnace troubles will be internal to it (not my expertise). The problems that could have to do with the circuit coming to it, will tend to show up as one tripping double breaker (out of as many as three a furnace might have), or a tripping breaker in the front of the furnace itself, or the furnace not running or not running on full heat. These symptoms can easily be from wires or contacts overheating at the breakers of the panel or of the furnace. Inspecting around those breakers will tend to show damage from such heat; replacement and other repair would then be needed. These areas are more subject to overheating because the high current that runs through these breakers is less tolerant of poor connections than lighter current is.
Room (zonal) electric heaters such as the fan-forced in-wall and the long baseboard radiators are run on circuits dedicated to heat only (perhaps switchable over to air conditioning), though the circuits can often have more than one heater and serve more than one room. Many in-wall heaters now have reset buttons (red or not) which keep the individual heater from functioning once it has overheated its interior; once this button is found (behind the grill), pushing it firmly in may let the heater work again, but the popping off may have been due to an unsafe condition that will recur unless addressed (dust accumulation, worn fan bearings, or the wrong grill).
Room heaters have elements that can burn out. Other components can also fail. When any of these heater parts stop it from running well, entire heater replacement is often easier than finding proper new parts. But sometimes the non-functioning of a heater is from an electrical wire connection gone bad or a bad thermostat. This would be the case if more than one heater is controlled by a thermostat and they all stop working at once, or if more than one room's heaters stop at the same time. (But it could be the case with just one room with one heater). The places to look for poor connectors (including those of the white wires, which are live, not neutrals) include: that circuit's breaker, its thermostat boxes, and where the cable for the heater(s) in question enters it or leaves a working heater.
Zonal electric heat provides thermostatic control for each heated area. Typically, these thermostats are factory calibrated so that the temperature settings stated on them correspond to the actual temperature they will maintain in the room. There will still be a lag of two or three degrees as the heater continues working before its heat has had a chance to affect the stat, or as the heater waits to come on because the coolness of the room air has not yet affected the stat to turn it on. People not familiar with such small but noticeable "swings" sometimes try to compensate for this by turning the stat way up or down, thinking the extreme settings will make things happen faster. They won't.
There are two ways that a thermostat can be inaccurate. One is that its calibration from the factory or over time has become five or even ten degrees off from the truth. Many have a small setscrew (painted in place so it won't move) that can readjust the calibration (judged by where the clicking sound occurs around the dial). However, many people are happy to ignore the strict temperatures stated on the stat and simply remember a setting that feels comfortable to them, perhaps marking this with a pencil.
The other inaccuracy of a thermostat is more extreme. This would be when its control of heat is either wildly erratic or occurs, if at all, only at the very low end of the scale -- the room definitely overheats. This tends to mean the thermostat is on its death bed, internally stuck on even when the dial is turned off. Beginning this century, however, some ultra-accurate thermostats relying on (AA) batteries will run their heaters all the time if the batteries have run down. For instance, some made under the brand "Ritetemp."
Some large living room areas use a low-voltage thermostat in conjunction with a relay. Calibration and "swing" problems for these can usually be addressed at the thermostat, whereas complete loss of control will mean the relay is bad. (Good luck finding and recognizing the relay.)
There is one further rare condition that can result in 240-volt zone heat running despite a thermostat being turned down. When the element of a heater shorts to the metal frame or fins near it, it can run constantly at a low wattage and not trip the breaker.