In thermoforming, flat plastic sheets are transformed into complex shapes by first softening by radiant heat transfer, and then by shaping. During the softening step, the sheet first bows while still solid, then sags while soft. In this article, we derive the heat flux distributions over both faces of a bowing or sagging sheet, along with the corresponding temperature profiles through and across the bowing or sagging sheet. These predictions can help plastics engineers to present a sheet of uniform temperature to a thermoforming mold. A worked example is included to show how to use the results.