The choke is that odd box on the side of the head. When it's cold, it allows the intake vacuum to pull raw gas out of the carb bowl. As it warms up, it starts giving a mix of gas and air. When it gets hot, it stops giving anything.
You will probably need to clean out the choke. Do not take apart the choke box!!
I cleaned mine by spraying WD-40 into the choke box, then alternatly heating and cooling it in the kitchen sink. Flushing it with water got all sorts of rust and grime out of it, and eventually the plunger inside started moving again. You should be able to noticably change the flow from one passage to another by varying the temp.