Transient infrared transmission spectroscopy is a new method that can acquire analytically useful transmission spectra from moving, optically thick solids. No sample preparation is required. The spectra are of sufficient quality for accurate quantitative compositional analysis. The method works by the creation of a thin, short-lived, chilled layer at the sample surface. Blackbody-like thermal emission from the bulk of the sample is selectively absorbed as it passes through the chilled layer, so the transmission spectrum of the layer is superimposed on the observed thermal emission. Spectra of polycarbonate, beeswax, and copolymers of methyl and butyl methacrylate are presented. Compositional analysis of the methacrylate copolymers with a standard error of prediction of only 0.87 mol % is demonstrated.