That it is - or more accurately, it's your "electrically assisted choke". The choke itself is entirely mechanical, but the pulloff (for when the motor's warm" is electrically assisted. Here's the deal:
Inside that black cap is a spring-looking bimetal element just like the one in all the older-style house thermostats. When it's cold, it winds up tightly and when it's warm it loosens. When it winds up (cold), it closes the choke plate at the top of the carburetor, inside the air cleaner (take the air cleaner off to see it) so's to enrich the fuel mixture - the motor needs a richer mixture to keep running when it's cold.
When it warms up (that red wire connects to a tiny heating element inside the black cap, and that little heating element runs any time the key is turned on), the motor doesn't want that rich a mixture (it'll flood), so the springy dude loosens and that opens the choke plate at the top of the carburetor to lean out the fuel mix.
You can only reasonably adjust that choke cap by taking the air cleaner off. With the engine dead cold (sat overnight), the choke plate should close fully and kinda' snugly but not really tightly. It should close with enough force to hold a pencil in place, but not a whole lot more than that - it shouldn't, for example, hold a screwdriver in place. You adjust that force by loosening those three screws and rotating the black cap.
Then when the motor's warmed up, the choke plate should be fully open... which should happen entirely automatically.
With the choke plate closed, your idle speed should follow the fast-idle cam. With the choke plate open, when you tap on the gas pedal the fast-idle cam should drop free and the idle speed should then be controlled by the low-idle screw.
Let's get that choke pulloff (the black cap) adjusted correctly & take it from there. That's probably part & parcel of the problem at this point. It's possible it's been hurt (rust or the heating element burnt out), but it's a LOT more likely that it only needs adjustment.