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Abstract New facilities such as the National Ignition Facility and the Linac Coherent Light Source have pushed the frontiers of high energy-density matter. These facilities offer unprecedented opportunities for exploring extreme states of matter, ranging from cryogenic solid-state systems to hot, dense plasmas, with applications to inertial-confinement fusion and astrophysics. However, significant gaps in our understanding of material properties in these rapidly evolving systems still persist. In particular, non-equilibrium transport properties of strongly-coupled Coulomb systems remain an open question. Here, we study ion-ion temperature relaxation in a binary mixture, exploiting a recently-developed dual-species ultracold neutral plasma. We compare measured relaxation rates with atomistic simulations and a range of popular theories. Our work validates the assumptions and capabilities of the simulations and invalidates theoretical models in this regime. This work illustrates an approach for precision determinations of detailed material properties in Coulomb mixtures across a wide range of conditions.