We measure the temperature distribution in a biased single-layer graphene transistor using Raman scattering microscopy of the 2D-phonon band. Peak operating temperatures of 1050 K are reached in the middle of the graphene sheet at 210 kW cm(-2) of dissipated electric power. The metallic contacts act as heat sinks, but not in a dominant fashion. To explain the observed temperature profile and heating rate, we have to include heat flow from the graphene to the gate oxide underneath, especially at elevated temperatures, where the graphene thermal conductivity is lowered due to umklapp scattering. Velocity saturation due to phonons with about 50-60 meV energy is inferred from the measured charge density via shifts in the Raman G-phonon band, suggesting that remote scattering (through field coupling) by substrate polar surface phonons increases the energy transfer to the substrate and at the same time limits the high-bias electronic conduction of graphene.