The overall heating of satellites operating in low orbit, essentially due to direct radiation from the sun and terrestrial albedo, and the planetary radiation, is well studied, but little is found specifically on transparent plates used for windowing spacecrafts. The most historic material of choice is fused silica, as in the cupola of the International Space Station; more recently, acrylic glass is being used, but its refractive properties are poorly documented. Starting from Maxwell’s laws, the effects of electromagnetic waves incident on multilayer windows composed of panes of fused silica or acrylic glass, or a composition of these, are analyzed. Using data of refractive index from the literature, which however are incomplete and sometimes contradictory, the problem is addressed by distinguishing the frequency of the radiation, because this affects the transmissibility and absorption of each material; moreover, the frequency content of the radiation of the solar and terrestrial albedo is different from that of the planet. Worked examples show that fused silica allows most radiation to pass directly through; absorption occurs in such a thin surface layer that it can be modeled as a boundary condition. Acrylic glass, on the other hand, is characterized by absorption depending on the thickness; this can potentially increase its temperature, posing a problem since the mechanical properties decay at temperatures above 100 °C. This study represents a key step to analyze the thermal problem for space windows, of considerable interest since glazing can fail due to thermal shocks, constrained thermal variations, or temperature concentrations.