This paper introduces a model predictive control (MPC) strategy for solid oxide fuel cell (SOFC) systems, introducing thermal stress-aware power modulation. The proposed MPC approach incorporates a temperature rate-of-change constraint to manage local temporal and spatial temperature gradients in the SOFC during transient power modulation. The study evaluates the sensitivity and effectiveness of the temperature rate-of-change constraint under four different constraint parameter sets, spanning a range from fast to slow power modulation. A one-dimensional spatially discretised SOFC model is employed in the simulations to assess the resulting local temperature gradients. The results of this paper indicate that the proposed MPC strategy enhances transient power tracking performance compared to the conventional approach of using an electrical current rate-of-change constraint with 1%–17%, without a significant increase in the local temporal and spatial temperature gradients in the SOFC.