Might as well jump in too LOL.
The heat flapper works in my 49 216 thusly:
Cold engine: The bi-metal spring is at it's full compressed state which pulls the flapper valve "open" and directs at least half the exhaust gases up into a chamber just under the imtake mainfold directly under the carb. This heats the chamber and cast surfaces around it. One of these surfaces is the bottom of the intake manifold. When fuel/air dropletts hit this surface the heated base plate helps to atomize the fuel/air mixture which makes for a better more complete ignition. This also lessens excess fuel into the cylinder which can make it's way past the rings diluting the crankcase oil.
The counter weight on the other end of the flapper rod has it's rounded side up.
Warm engine: As the engine warms up the bi-metal spring starts to lose it's tightness and begins to unwind a little. This relieves it's spring pressure on the flapper valve which begins to "close". Due to the design of the counter weight and flapper valve the on rushing exhaust gases help to close it further and as the spring tension lessons the gasses continue to push the flapper closed as they exit.
In the closed position exhaust gases are redirected straight out the exhaust pipe and greatly lessens the amount of hot gases that get into the heat chamber under the intake manifold.
Engine at operating temp: The bi-metal spring is at it's weakest point and is applying very little to ziltch spring pressure to the flapper valve. This allows the counter weight and exiting exhaust gases to hold the fllapper valve in the closed position. Most if not all exhaust gases are directed straight out to the exhaust pipe and only minimal gases get around the flapper into the heat chamber under the intake manifold.
I've noticed that the flapper will still try to open some on my 216 when it's warmed up to operating temp at idle but when I increase the rpm from idle the gases will fully close the flapper and keep it closed for as long as the rpm is higher than idle. Once rpm is dropped back to idle the flapper will move alittle towards open but not fully like when it's cold. It could be that the bi-metal spring is alittle too taught but I've left it like this for going on 22k miles and the 49 3100 with a very tired 216 avgs 12.5 mpg and starts and runs all year long, all 4 seasons reliably.
re. OP. What position is the flapper stuck? Open (weight round side up) or close (weight round side on it's side).
Being stuck closed is better than stuck open but a working flapper is best.
Good luck
Dave