If the fan is set to “On,” it can keep circulating room-temperature air between heating cycles. Set the thermostat to “Heat” and the fan to “Auto,” then check whether the filter is dirty and supply vents are open. A brief cool draft at startup may be normal, but air that stays cold can point to an ignition, airflow, or safety-control problem.
If those simple checks do not restore heat, turn the system off and request furnace repair. Leave gas and electrical components to a qualified technician.