This paper studies the impact of two significant aspects, namely fuel cell (FC) degradation and thermal management, over the performance of an optimal and a rule-based energy management strategy (EMS) in a fuel cell hybrid electric vehicle (FCHEV). To do so, firstly, a vehicle model is developed in simulation environment for a low-speed FCHEV composed of a FC stack and a battery pack. Subsequently, deterministic dynamic programming (DP), as an optimal strategy, and bounded load following strategy (BLFS), as a common rule-based strategy, are utilized to minimize the hydrogen consumption while respecting the operating constraints of the power sources. The performance of the EMSs is assessed in different scenarios. The first objective is to clarify the effect of FC stack degradation on the performance of the vehicle. In this regard, each EMS determines the required current from the FC stack for two FCs with different levels of degradation. The second objective is to evaluate the thermal management contribution in improving the performance for the new FC compared to the considered cases in scenario one. In this respect, each strategy deals with determining two control variables (FC current and cooling fan duty cycle). The results of this study indicate that negligence of adapting to the PEMFC health state, as the PEMFC gets aged, can increase the hydrogen consumption up to 24.8% in DP and 12.1% in BLFS. Moreover, the integration of temperature dimension into the EMS can diminish the hydrogen consumption by 4.1% and 5.3% in DP and BLFS respectively.