Recent research in price-based Mobile Edge Computing (MEC) has predominantly aimed at maximizing edge server revenue by efficiently allocating computing resources. While this operational approach has certainly strengthened the edge computing industry, the practical deployment scenario's impact on server hardware lifespan has not been fully explored. In this paper, we introduce a novel server pricing strategy that accounts for the influence of CPU temperature on the server's longevity, all while ensuring the quality of service requirements for time-sensitive User Equipments (UEs). Leveraging these insights, we establish an MEC system model with a single MEC server and multiple UEs, which we then formulate as a Stackelberg game. We derive two closed-form solutions considering various UEs' conditions, closely aligning with the expectations of time-sensitive UEs. Our simulation results showcase the effectiveness of our proposed method in safeguarding hardware equipment while minimizing revenue loss.