The convective temperature is found on a Skew-T Log-P diagram by dropping a parcel of air dry adiabatically from the CCL (Convective Condensation Level) to the surface and reading off the new temperature once the parcel reaches the surface.
The convective temperature is the temperature the surface of the earth must warm to in order for thunderstorms to occur in the absence of synoptic forcing mechanisms (i.e. development of afternoon "air-mass" thunderstorms). Forecasting the convective temperature is most relevant in the barotropic summer time environment. The convective temperature is most likely to be reached in the late afternoon hours due to cumulative solar heating. Once the convective temperature is reached, air parcels can rise freely to the CCL (Convective Condensation Level) and will thus be free to rise due to positive buoyancy throughout the troposphere to develop thunderstorms.
The strength of the "cap" determines if the convective temperature will be reached. When the cap is very strong, the convective temperature will be higher than the high temperature for that day and thus no storms develop. The amount of low level moisture also determines if the convective temperature will be reached. The CCL increases in height as the average PBL dewpoint decreases. A higher CCL results in a higher convective temperature.
Dynamic upward forcing lowers the theoretical convective temperature since parcels of air can be "forced" or brought closer to the CCL by lifting mechanisms such as fronts, low level WAA and low level convergence.