The performance and scaling of graphene-based electronics(1) is limited by the quality of contacts between the graphene and metal electrodes(2-4). However, the nature of graphene-metal contacts remains incompletely understood. Here, we use atomic force microscopy to measure the temperature distributions at the contacts of working graphene transistors with a spatial resolution of similar to 10 nm (refs 5-8), allowing us to identify the presence of Joule heating(9-11), current crowding(12-16) and thermoelectric heating and cooling(17). Comparison with simulation enables extraction of the contact resistivity (150-200 Omega mu m(2)) and transfer length (0.2-0.5 mu m) in our devices; these generally limit performance and must be minimized. Our data indicate that thermoelectric effects account for up to one-third of the contact temperature changes, and that current crowding accounts for most of the remainder. Modelling predicts that the role of current crowding will diminish and the role of thermoelectric effects will increase as contacts improve.