In protein unfolding simulations, elevated temperature, significantly exceeding the melting temperature Tm, provides an important means to accelerate unfolding to a computationally accessible time range. This procedure is based on the assumption that protein thermal unfolding has Arrhenius behavior and therefore that increasing temperature does not alter the protein unfolding pathways. However, in nature, proteins can show non-Arrhenius behavior and, in practice, overly fast unfolding in high-temperature simulations can result in difficulties in identifying unfolding intermediates and distinguishing their relative stabilities. In this paper, we describe simulations of two WW domains, small protein domains that have a three-stranded β-sheet structure. Simulations were carried out at several temperatures ranging from 300 K to 500 K, starting from folded structures. The results demonstrate the temperature dependence of the unfolding pathways, showing that to obtain unfolding pathways corresponding to those observed in experiments, the elevation of the simulation temperature has to be controlled. Based on trajectory analysis, we proposed a qualitative criterion for judging when an elevated temperature is acceptable or not, namely, that the temperature must be such that the native folded state is sampled substantially before protein unfolding begins. While depending on force field parameters and protein fold complexity, this criterion can be quantified to obtain the upper bound of an "acceptable elevated temperature", which was observed to be dependent on the thermostabilities of the two WW domain proteins.