In condensed matter, scattering processes determine the transport of charge carriers. In case of heterostructures, interfaces determine many dynamic properties like charge transfer and transport and spin current dynamics. Here we discuss optically excited electron dynamics and their propagation across a lattice-matched, metal-metal interface of single crystal quality. Using femtosecond time-resolved linear photoelectron spectroscopy upon optically pumping different constituents of the heterostructure we establish a technique which probes the electron propagation and its energy relaxation simultaneously. In our approach a near-infrared pump pulse excites electrons directly either in the Au layer or in the Fe layer of epitaxial Au/Fe/MgO(001) heterostructures while the transient photoemission spectrum is measured by an ultraviolet probe pulse on the Au surface. Upon femtosecond laser excitation, we analyze the relative changes in the electron distribution close to the Fermi energy and assign characteristic features of the time-dependent electron distribution to transport of hot and non-thermalized electrons from the Fe layer to the Au surface and vice versa. From the measured transient electron distribution we determine the excess energy which we compare with a calculation based on the two-temperature model and takes diffusive electron transport into account. On this basis we identify a transition from a super-diffusive to a diffusive transport regime to occur for a Au layer thickness of 20-30~nm.