There is clear evidence that the West Antarctic Ice Sheet is contributing to sea-level rise. In contrast, West Antarctic temperature changes in recent decades remain uncertain. West Antarctica has probably warmed since the 1950s, but there is disagreement regarding the magnitude, seasonality and spatial extent of this warming. This is primarily because long-term near-surface temperature observations are restricted to Byrd Station in central West Antarctica, a data set with substantial gaps. Here, we present a complete temperature record for Byrd Station, in which observations have been corrected, and gaps have been filled using global reanalysis data and spatial interpolation. The record reveals a linear increase in annual temperature between 1958 and 2010 by 2.4+/-1.2°C, establishing central West Antarctica as one of the fastest-warming regions globally. We confirm previous reports of West Antarctic warming, in annual average and in austral spring and winter, but find substantially larger temperature increases. In contrast to previous studies, we report statistically significant warming during austral summer, particularly in December-January, the peak of the melting season. A continued rise in summer temperatures could lead to more frequent and extensive episodes of surface melting of the West Antarctic Ice Sheet. These results argue for a robust long-term meteorological observation network in the region.