It's probably more accurate to think of thermals as vertical cylinders. Air detrained from the thermal edges is cooled, and cannot be recirculated into the thermal except at the ground. Vortex rings of the size of thermals are not observed. The strength of thermals is controlled by the amount of sunlight and the surface conditions. If the surface is wet or moisture is being emitted by healthy plants, a larger fraction of the incoming heat from the sun will be used to evaporate water than to heat the air.
Water vapor does contribute to buoyancy, but less than heat does.
So far I've described the situation in the middle of a day with light wind and high pressure. If the barometric pressure is low, there will likely not be an inversion to define the boundary layer top. They do, but not predictably. Their rotation is determined by local terrain. Rotational velocity in the core of a typical thermal is small compared to the vertical velocity.