incoming gas yes goes to a regulator that goes to a valve that is controlled by a safety valve that allows gas to flow to a burner that is controlled by a thermostat,sometimes controlled by a flame switch that goes to an orifice that regulates the size of the flame got that

Think of a clogged vent, congested air flow,will cause the thermostats to trip early/often .the exhaust vent in the bottom is where you start.And you may have to disassemble unit to get to the internals,fan ect.