If your furnace is not keeping your house at the temperature to which you set it, then you have a problem somewhere in your heating system. The issue may be with the furnace itself, but it also may come from a number of other sources. Before you spend money on repair professionals, try to diagnose the problem yourself so that you have a better idea of what kind of help you need.
Before you assume that anything is wrong with one of the parts of the system, consider the possibility that your furnace is the wrong size. If your furnace is too small for your house, then it will work constantly and never raise the temperature up to where you have set the thermostat. Having a furnace that is too big for your house can also be a problem. A furnace doesn't heat all the air in the house -- it just heats the air that the ducts bring to it. An over-sized heater can heat the air too fast, raising the temperature near the thermostat faster than that in the rest of the house. Once the thermostat reads enough warmth, it shuts off, leaving the rest of the house too cold.
Your thermostat could be broken and misreading the temperature as being higher than it really is. This would cause the furnace to shut off before it actually warms the house enough. If your house has a programmable thermostat, a fault in it could cause the thermostat to turn the furnace off and on at inappropriate times. Use a thermometer to check the temperature in the air next to the thermostat to see if the thermostat is reading correctly.
The furnace circulates the air it warms through the house by means of a fan. It is supposed to stay on for two to three minutes after the furnace shuts off in order to push the last of the warm air out into the house. If the fan stays on after this period, then it starts pushing cold air into the house, which could account for the uneven temperature control. This problem can be caused by an improper fan delay setting or a problem with its controls.
Condensing Furnace Problems
If you have a condensing furnace that turns on for longer than five seconds but shuts off again before reaching the right temperature, then you may have a plugged condensate drain. The condensate pump reservoir might be full instead. This can cause the furnace to shut off.
If your furnace has a pilot light that tries to ignite but goes out instead, you may have a problem with the pilot light hardware or sensors. If your furnace uses an electronic ignition and it does not ignite, the igniter or control board may be bad. There are a number of other potential causes as well, such as faulty gas valves and control board faults, but these cannot be easily diagnosed except by professionals.