yes, reads like you shouldn't shut it off if you are just going to be restarting it again without letting it cool down more
There are a few things it could be, i would pull out the spark plugs and have a look at each one to see if they tell you anything about cylinders, could have coolant getting in or oil or extra fuel.
You may want to change the ECT sensor(2 wire sensor) just on spec, $7, this tells the computer(not dash gauge) the coolant temp.
The computer bases Choke mode on this sensor, when coolant is cold computer runs engine rich with advanced spark timing until it warms up.
If this happened with warm engine it would run very rough until ECT sensor reported correct coolant temp.
IAC valve may not be responding correctly, this is a mechanical valve that control air flow into intake at idle and lower RPMs, if this valve is sticking it would cause stumbling.
Although this should happen cold or warm but.............could just happen warm.
IAC is easy to clean.