In this work, we report on hot carrier diffusion in graphene across large enough length scales that the carriers are not thermalized across the crystal. The carriers are injected into graphene at one site and their thermal transport is studied as a function of applied power and distance from the heating source, up to tens of micrometers away. Superconducting contacts prevent out-diffusion of hot carriers to isolate the electron-phonon coupling as the sole channel for thermal relaxation. As local thermometers, we use the amplitude of the universal conductance fluctuations, which varies monotonically as a function of temperature. By measuring the electron temperature simultaneously along the length we observe a thermal gradient which results from the competition between electron-phonon cooling and lateral heat flow.