The integration of a solid oxide electrolysis cell (SOEC) with a photovoltaic (PV) system presents a viable method for storing variable solar energy through the production of green hydrogen. To ensure the SOEC's safety and longevity amidst dramatic fluctuations in solar power, control strategies are needed to limit the temperature gradients and rates of temperature change within the SOEC. Recognizing that the reactant supply influences the current, a novel control strategy is developed to modulate heat generation in the SOEC by adjusting the fuel flow rate. The effectiveness of this strategy is assessed through numerical simulations conducted on a coupled PV-SOEC system using actual solar irradiance data, recorded at two-second intervals, to account for rapid changes in solar exposure. The results indicate that conventional control strategies, which increase airflow rates, are inadequate in effectively suppressing the rate of temperature variation in scenarios of drastic solar power changes. In contrast, our proposed strategy demonstrates successful management of the SOEC's heat generation, thereby reducing the temperature gradient and rate of variation within the SOEC to below 5 K/cm and 1 K/min, respectively.