The process of radiative heating of a moving polymeric sheet has been solved by numerical simulation. The heating was accomplished as the moving sheet was stretched over a hot roll having a corrugated surface. Radiative and convective heat losses were taken into account in the simulation. The heating process was subdivided into two time periods. The first of these periods occurred as the moving sheet approached the heated roll prior to making contact with it. During the second period, the moving sheet was in contact with the tips of the corrugations of the roll surface. The analysis of the problem led to a system of integro-differential equations. These equations were solved numerically to determine the timewise temperature variation of the moving sheet. It was found that the heating of the sheet prior to its contact with the roll surface is negligible. As the sheet passed over the roll, a transient heating period ensued which ultimately gave rise to a steady-state temperature of the sheet. For all of the investigated cases, steady state was achieved within 30 s from the onset of contact.