An exact solution is derived to the one‐dimensional, time‐dependent, heat‐conduction equation for a two‐layer, semi‐infinite, composite solid with uniform heat generation in the surface layer, no heat transfer through the surface plane, and uniform initial temperature. The interface between the two layers is assumed to have no thermal contact resistance. This solution enables a discussion of the ideality with which a step‐function electric current in a metallic foil can generate a step‐function heat flux into a contacting semi‐infinite solid. Previous measurements of thermal diffusivity (based on the above conditions) have relied on the idealized constant‐flux solution for data reduction. It is shown here that the temperature errors in the substrate arising from nonideality of the constant‐flux boundary condition increase with depth into the substrate, foil thickness, and decreasing thermal conductivity/diffusivity of the substrate.