This paper is aimed at investigating the effect of solar radiation on the inner ambient behind a building wall with facing material of different colors. At the wall outer-surface, the incident radiation results in a reflected radiation into the outer ambient depending on the reflection-coefficient of the wall-facing material and a transmitted radiation in the wall, whose intensity decays through its propagation in the wall depending on the absorption-factor of the wall material. At the wall inner-surface, the transmitted-radiation results in a reflected-radiation inside the wall and a penetrated-radiation into the inner- ambient of the wall. The sequence of radiation-propagation is continued with incidence, reflection and penetration at the wall inner-surface as well as incidence and reflection at the wall outer-surface.. To the author's knowledge, this sequence of radiation-propagation is evaluated numerically -for the first time- in the present paper. The absorbed-radiation intensity in the wall and the penetrated-radiation intensity into inner-ambient are calculated for varying albedo-values according to color of the facing-material and different values of absorption-coefficient of the wall material. The proposed method justifies that the wall-facing materials with white color realize heat-protection in summer and heat-insulation in winter with a subsequent improvement of the thermal comfort. The temperature of the inner-ambient with facing-material of dark-color is higher than that with white-color in agreement with previous findings based on measurements for small-scale building walls by others and measurements by the author for local buildings in Assiut city, Egypt as well as predictions using computer software packages.