We report the thermal conductance G of Au/Ti/graphene/SiO2 interfaces (graphene layers 1 or = n or = 10) typical of graphene transistor contacts. We find G approx. = 25 MW/sq m/K at room temperature, four times smaller than the thermal conductance of a Au/Ti/SiO2 interface, even when n = 1. We attribute this reduction to the thermal resistance of Au/Ti/graphene and graphene/SiO2 interfaces acting in series. The temperature dependence of G from 50 , or = T or = 500 K also indicates that heat is predominantly carried by phonons through these interfaces. Our findings suggest that metal contacts can limit not only electrical transport but also thermal dissipation from submicrometer graphene devices.