Surface convection and refractive index effects are examined during transient radiative heating or cooling of a grey semitransparent layer with internal absorption, emission and conduction. Each side of the layer is exposed to hot or cold radiative surroundings, while each boundary is heated or cooled by convection. Emission within the layer and internal reflections depend on the layer refractive index. The reflected energy and heat conduction distribute energy across the layer and partially equalize the transient temperature distributions. Solutions are given to demonstrate the effect of radiative heating for layers with various optical thicknesses, the behavior of a layer heated by radiation on one side and convectively cooled on the other, and a layer heated by convection while being cooled by radiation. The numerical method is an implicit finite difference procedure with non-uniform space and time increments. The basic method developed in earlier work is expanded to include external convection and incident radiation.