Full hybrid electric vehicles have proven to be a midterm viable solution to fulfil stricter regulations, such as those regarding carbon dioxide abatement. Although fuel economy directly benefits from hybridization, the use of the electric machine for propulsion may hinder an appropriate warming of the aftertreatment system, whose temperature is directly related to the emissions conversion efficiency. The present work evaluates the efficacy of a supervisory energy management strategy based on Equivalent Minimization Consumption Strategy (ECMS) which incorporates a temperature-based control for the thermal management of the Three-Way Catalyst (TWC). The impact of using only the midspan temperature of TWC is compared against the case where temperature at three different sampling points along the TWC length are used. Moreover, a penalty term based on TWC temperature has been introduced in the cost functional of the ECMS to allow the control of the TWC temperature operating window. In fact, beyond a certain threshold, the increase of the engine load, requested to speed up TWC warming, does not translate into a better catalyst efficiency, because the TWC gets close to its highest conversion rate. A gasoline P2 parallel full hybrid powertrain has been considered as test case. Results show that the effects of the different calibrations strategies are negligible on the TWC thermal management, as they do not provide any improvements in the fuel economy nor in the emissions abatement of the hybrid powertrain. This effect can be explained by the fact that the charge sustaining condition has a greater weight on the energy management strategy than the effects deriving from the addition of the soft constraints to control the TWC thermal management. These results hence encourage the use of simple setups to deal with the control of the TWC in supervisory control strategies for full hybrid electric vehicle