Gasoline Full Hybrid Electric Vehicles (FHEVs) are considered among good candidates as cost-effective solution to comply with upcoming emissions legislation. However, several studies have highlighted that frequent start-and-stops worsen the hydrocarbon tailpipe emissions, especially when the light-off temperature of the three-way catalyst (TWC) has not been reached. In fact, strategies only addressing the minimization of fuel consumption tend to delay engine activation and hence TWC warming, especially during urban driving. Goal of the present research is therefore to develop an on-line powertrain management strategy accounting also for TWC temperature, in order to reduce the time needed to reach TWC light-off temperature. A catalyst model is incorporated into the model of the powertrain where torque-split is performed by an adaptive equivalent consumption minimization strategy (a-ECMS). The developed a-ECMS operates on a domain of power-split combinations between electric machine and internal combustion engine, which, aside from satisfying the torque demand, also ensure a controlled ICE torque derivative as well as a controlled ICE start-and-stop frequency. Hence, the algorithm, which is extended for TWC thermal management, incorporates a penalty on the deviation of the TWC temperature from its optimal temperature range. The strategy has been tested on a gasoline P2 FHEV platform whose components (internal combustion engine, electric machine, battery and three-way catalyst) have been experimentally characterized. In particular, the battery current limitations have been modelled as a function of energy transfer. The effects deriving from the strategy, in terms of fuel consumption and catalyst efficiency, have been analyzed on the WLTC (Worldwide harmonized Light vehicles Test Cycles), the new homologation cycle enforced by European legislation. The control algorithm enhances a sufficient catalyst heating within a timespan comparable to the one of a conventional ICE case. The control strategy that integrates TWC thermal management causes an increase of about 2% in fuel consumption, compared to an only fuel economy-oriented a-ECMS strategy.