An upper bound on annual average energy in the Earth’s winds is calculated via the formalism of finite‐time thermodynamics. The Earth’s atmosphere is viewed as the working fluid of a heat engine where the heat input is solar radiation, the heat rejection is to the surrounding universe, and the work output is the energy in the Earth’s winds. The upper bound for the annual average power in the Earth’s winds is found to be 17 W/m2, which can be contrasted with the actual estimated annual average wind power of 7 W/m2. Our thermodynamic model also predicts the average extreme temperatures of the Earth’s atmosphere and can be applied to wind systems on other planets.