The air is heated in the choke furnace (exhaust manifold ) and rises through metal tube with the insulated sheath to the choke bimetal heat actuated spring. Heat rises. The lower port on the choke furnace is for fresh cooler air which is drawn in displacing the rising heated air. The cooler fresh air comes from the carburetor by way of the uninsulated metal tube (not necessary to be insulated) and connected to the carb by a rubber hose (because it doesn't get hot like the heated side). I hope this helps understand the loop.
Yes, heated air does rise relative to cooler air. However, with the size of tubing involved in this application, convection alone would not produce sufficient flow. The amount of force from convection would not be sufficient to overcome the amount of vacuum present on the inlet end of the tube (the connection on the air horn portion of the carb), which would result in flow AWAY from the thermostat housing. Thus, a stronger vacuum source is required at the choke housing to pull air toward the choke housing. And that vacuum is provided as shown in the illustration attached below.
These images come from the 1968 shop manual. I believe the choke is identical to the 1967 choke. If not physically identical, operation would be the same. Vacuum from the intake manifold is routed through the carb to the choke housing. It is this vacuum source which is drawing air through the choke heat tube, starting at the air horn inlet, making its way downward through the manifold connection and upwards until it reaches the choke housing. Some chokes such as this have an assist piston, but others that rely entirely on the thermostatic spring have vacuum routed the same way. I've included the description of operation as explained in the manual; I'm sure it will make more sense than my brief explanation.
The only thing it doesn't explain is the inlet connection to the air horn - why connect that end to what appears to be a vacuum source?
The reason is, the engineers wanted a source of clean, filtered air to prevent dust from clogging the tubing and the choke mechanism (and the carb passages too). Instead of having an inlet right at the manifold and adding a small filter, they used another filter that was already present - the one cleaning the air entering the engine. So they tapped into an area in which air has passed through the filter. This area is at a lower pressure than the air in the engine compartment, but that's not a problem, since the choke housing is ported to an even stronger source of vacuum, thus ensuring flow goes the correct direction.
Ultimately, while this system works, it is a bit complicated and is subject to leaks, kinked tubing, and air filters that don't quite keep everything out that they're supposed to. Thus the eventual switch to electrically heated chokes.