The Gulf of Mexico (GOM) receives heat from the Caribbean Sea via the Yucatan-Loop Current (LC) system, and the corresponding ocean heat content (OHC) is important to weather and climate of the continental United States. However, the mechanisms that affect this heat influx and how it is distributed in the Gulf have not been studied. Using the Princeton Ocean Model, the authors show that a steady, uniform westward wind in the Gulf increases (~100 KJ cm-2) the upper OHC (temperature T > 18°C) of the Gulf. This is because wind increases the water exchange between the Gulf and the Caribbean Sea, and the heat input into the Gulf is also increased, by about 50 TW. The westward heat transport to the western Gulf is ~30 TW, and a substantial portion of this is due to wind-induced shelf currents, which converge to produce downwelling near the western coast. Finally, eddies are effective transporters of heat across the central Gulf. Wind forces larger LC and rings with deeper isotherms. This and downfront-wind mixing on the southern side of anticyclonic rings, northward spread of near-zero potential vorticity waters, and downwelling on the northern shelf break result in wide and deep eddies that transport large OHCs across the Gulf.