Does thermal bubble initiated in WRF dissipate over time?
After initialization the model calculates forward in time ncluding all physical processes represented by your setup of WRF. This probably means that the warm air will rise and thereby trigger the supercell thunderstorm. Cape can be calculated for a parcel starting at any height. If the bubble (warm anomaly) is present at the surface, and you are interested in the so-called surface-based Cape, then I would set the temperature to the environmental temperature + the warm anomaly. Why not try out both and see what the difference is? This would give you an idea of the vertical forcing magnitude of the warm anomaly.