Recent studies highlight that oceanic motions associated with horizontal scales smaller than 50 km, defined here as submesoscales, lead to anomalous vertical heat fluxes from colder to warmer waters. This unique transport property is not captured in climate models that have insufficient resolution to simulate these submesoscale dynamics. Here, we use an ocean model with an unprecedented resolution that, for the first time, globally resolves submesoscale heat transport. Upper-ocean submesoscale turbulence produces a systematically-upward heat transport that is five times larger than mesoscale heat transport, with winter-time averages up to 100 W/m2 for mid-latitudes. Compared to a lower-resolution model, submesoscale heat transport warms the sea surface up to 0.3 °C and produces an upward annual-mean air-sea heat flux anomaly of 4-10 W/m2 at mid-latitudes. These results indicate that submesoscale dynamics are critical to the transport of heat between the ocean interior and the atmosphere, and are thus a key component of the Earth's climate.