We have central heating (gas heated) and when we turn the heat on, the house heats up for just a couple of minutes and then the heat turns cool. Although we have it set to "automatic" rather than "on", it never shuts off because obviously it's trying to warm the house and isn't reaching the set temperature. The pilot light is lit, so what else could cause this? I assume it's not a thermostat problem, otherwise it would shut off.

The burners may be going off on a limit switch, check your filters and any belts that may be on the blower if it is belt drive. Next check your heat anticipator in the thermostat, this is a sliding arrow on a numbered scale under the cover of mechanical thermostats, if is set too low it will cause the gas valve to shut off to soon, try 4.5 on the scale, Good luck, Mike