Each type of gas furnace works differently. Therefore, the sequence of operation or how the gas furnace works will work differently for each gas furnace type. Since you have a standing pilot gas furnace, it will work differently from an electronic ignition gas furnace.
How a Standing Pilot Gas Furnace Works - How a Gas Furnace Works
This is a safety for standing pilot gas valves. It prevents the main valve from opening unless a pilot light is present to light the main burners. That keeps raw un-ignited gas from being spewed out into the atmosphere. If that happened, the gas becomes an explosive hazard. Aside from that, the other safeties in the system include a high limit safety. The high limit safety opens if the heat exchanger temperature reaches a preset temperature.
This is defined by the engineer of the furnace and prevents temperatures from exceeding safety limitations. Other safeties, including limit switches, can be on the blower in case the fan overheats. A spill switch (also a limit switch) near the draft hood if the flue or chimney fails in some way. All these limits are in series with the operation of the main gas valve. Or the pilot safety on the gas valve itself and prevent a safety hazard if it exists.
How a Gas Furnace Works - Fire It Up!
If all the safeties are good and the main burner ignites then the furnace begins heating up. As it heats up a fan limit control senses the heat. When it reaches the adjustable set temperature it engages the blower. The fan kicks on and distributes the heat through the duct system.
Everything continues to run until the thermostat satisfies. When the thermostat satisfies the main burners shut down but the blower continues running. The blower continues running to cool the furnace down. It also continues to run to use the usable heat still inside the furnace and ductwork.
If the thermostat is properly set up the heating anticipator will end the call for heat before the thermostat satisfies taking into account the blower continues to run to cool down the furnace.
The anticipator prevents overheating or overshooting the thermostat set point as the blower expels the additional heat inside the furnace after gas main burners shut down. When the additional heat is expelled the fan limit control shuts down the blower and the system is on standby until the thermostat again makes a call for heat.
How a Gas Furnace Works - HVAC Heating