A three-dimensional numerical model is described to study and investigate the impact of the Orissa super cyclone on the ocean. The forcing mechanism in the model is the wind stress derived from moving cyclonic storm/satellite winds. Numerical experiments have been performed using the model in order to understand the dynamics and thermodynamics of the ocean owing to the cyclone crossing the Paradip coast. The model was used to simulate the thermal response of the ocean to study the surface cooling and the surge associated with the cyclone. A net decrease in sea-surface temperature of about 5–6 °C and a peak surge of over 6 m were simulated when the storm moved over the Orissa coast. The model computations were compared with the satellite data (TMI—Tropical Rainfall Measuring Mission [TRMM] Microwave Imager) available during the storm period. In the subsequent experiments, the variation of the ocean's response to the changes in the translation speed of the cyclone was examined. We conclude that the speed of the cyclone, which determines the resident time of the cyclone over the ocean, leaves an overwhelming influence on sea-surface cooling and surge generation.