We demonstrate experimentally nonequilibrium transport in unipolar quasi-1D hot electron devices reaching the ballistic limit at room temperature. The devices are realized with heterostructure engineering in nanowires to obtain dopant- and dislocation-free 1D-epitaxy and flexible bandgap engineering. We show experimentally the control of hot electron injection with a graded conduction band profile and the subsequent filtering of hot and relaxed electrons with rectangular energy barriers. The number of electrons passing the barrier depends exponentially on the transport length with a mean-free path of 200-260 nm, and the electrons reach the ballistic transport regime for the shortest devices with 70% of the electrons flying freely through the base electrode and the barrier reflections limiting the transport to the collector.