The thermal performance of a far-field radiative transistor made up of a VO2 base in between a blackbody collector and a blackbody emitter is theoretically studied and optimized. This is done by using the grey approximation on the emissivity of VO2 and deriving analytical expressions for the involved heat fluxes and transistor amplification factor. It is shown that this amplification factor can be maximized by tuning the base temperature close to its critical one, which is determined by the temperature derivative of the VO2 emissivity and the equilibrium temperatures of the collector and emitter. This maximization is the result of the presence of two bi-stable temperatures appearing during the heating and cooling processes of the VO2 base and enables a thermal switching (temperature jump) characterized by a sizeable variation of the collector-to-base and base-to-emitter heat fluxes associated with a slight change of the applied power to the base. This switching effect leads to the optimization of the amplification factor and therefore it could be used for thermal modulation purposes.