We investigate heat conduction and energy relaxation in an InAs semiconductor nanowire using a hybrid semiconductor–superconductor architecture. Local electronic temperatures are measured with an in-situ grown quantum dot thermometer, while controlled Joule heating is applied at different locations along the wire to probe the heat flow along the nanowire at sub-kelvin temperatures. With a one-dimensional heat transport model, we calculate an electron-phonon heat flow that scales as Q_{e-ph} T^2.6, which is in close agreement with the T^3 dependence predicted for a clean one-dimensional phonons coupled to the electron gas. We further estimate a characteristic length l_{eq} = 370 nm, beyond this length scale, phonon-mediated heat transport dominates over heat conduction in our nanowire. Our results provide a quantitative measure of energy relaxation mechanisms in a one-dimensional semiconductor and provide a framework for studying heat flow in low-dimensional nanostructures.