When it's in "hot start" mode there's a thermal coiled sprind insibe the inlet end of the exhaust that once heated pushes the lever on the exhaust side of the engine and disengages the choke thus starting without choke.
That sounds a lot like the 'electric choke' system that was used on a lot of US 4-barrel car carbies.
There was a bimetallic spring, as you describe, in a sealed Bakelite chamber that also held a 12V heating element, wired to operate when the ignition was switched on. So as the chamber heated up after the engine started, the bimetallic spring would pull the choke off. As the chamber cooled down slowly, the choke would only re-engage when the engine had cooled down too. The main failure mode of these units was the open-wire heating element would fail. The Briggs setup would avoid that problem.
