My home heater comes on, blows hot air for 10 to 15 minutes, then cold air until we turn it off. If we leave it off for about 30 minutes, it blows hot air again, for 10 to 15 minutes, then cold again. What do you think is the cause?

Could be many things. Thermostat heat anticipator setting,dirty air filter, some registers shut off allowing heat build up in furnace, weak or out of calibration high limit etc.