The discontinuity of a spin-current through an interface caused by spin-orbit coupling is characterized by the spin memory loss (SML) parameter δ. We use first-principles scattering theory and a recently developed local current scheme to study the SML for Au|Pt, Au|Pd, Py|Pt, and Co|Pt interfaces. We find a minimal temperature dependence for nonmagnetic interfaces and a strong dependence for interfaces involving ferromagnets that we attribute to the spin disorder. The SML is larger for Co|Pt than for Py|Pt because the interface is more abrupt. Lattice mismatch and interface alloying strongly enhance the SML that is larger for a Au|Pt than for a Au|Pd interface. The effect of the proximity-induced magnetization of Pt is negligible.