The West Spitsbergen Current (WSC) is the major source of heat and salt for the Arctic Ocean and the areas of deep convection in the Greenland Sea. The WSC current cools dramatically downstream. Hydrographic and velocity data from a 3-week, midwinter cruise off Spitsbergen are used to investigate the heat budget of the WSC and the mechanisms of cooling. The downstream divergence of mean heat flux in the WSC produces a heat loss of at least 1000¿400 W m-2 averaged over the width of the current. Approximately 350 W m-2 is lost to the atmosphere and 200 W m-2 is lost to melting ice over a region somewhat wider than the current. Cooling of the WSC to the atmosphere converts the inflowing Atlantic Water (AW) to Lower Arctic Intermediate Water, which is sufficiently salty to convect. Cooling by ice converts the AW to much fresher Arctic Surface Water, which is too light to convect. The relative importance of these two conversions is primarily controlled by the rate at which the wind advects ice from the Barents Sea over the WSC. The warmest water of the WSC is often observed 100--200 m below the surface. Despite the lack of direct contact with the surface, this warm core cools at about 800 W m-2 in our observations. This rate is too large to be caused by diapycnal diffusion. We suggest that the energetic eddy field in this area diffuses heat along the steeply sloping isopycnal surfaces that connect the warm core to the surface, renewing the surface layer several times per day. This is consistent with the very shallow surface mixed layers and high level of intrusions observed. We conclude that the surface layer of the WSC is cooled by the atmosphere and by ice from the Barents Sea and that isopycnal diffusion by mesoscale eddies continually renews this surface, thus cooling the interior of the WSC. The relative magnitude of these processes determines whether the inflowing warm, salty AW is converted to light, fresh surface water or salty, cold intermediate water.