The Saharan silver ant Cataglyphis bombycina is one of the terrestrial living organisms best adapted to tolerate high temperatures. It has recently been shown that the hairs covering the ant's dorsal body part are responsible for its silvery appearance. The hairs have a triangular cross-section with two corrugated surfaces allowing a high optical reflection in the visible and near-infrared (NIR) range of the spectrum while maximizing heat emissivity in the mid-infrared (MIR). Those two effects account for remarkable thermoregulatory properties, enabling the ant to maintain a lower thermal steady state and to cope with the high temperature of its natural habitat. In this paper, we further investigate how geometrical optical and high reflection properties account for the bright silver color of C. bombycina. Using optical ray-tracing models and attenuated total reflection (ATR) experiments, we show that, for a large range of incidence angles, total internal reflection (TIR) conditions are satisfied on the basal face of each hair for light entering and exiting through its upper faces. The reflection properties of the hairs are further enhanced by the presence of the corrugated surface, giving them an almost total specular reflectance for most incidence angles. We also show that hairs provide an almost 10-fold increase in light reflection, and we confirm experimentally that they are responsible for a lower internal body temperature under incident sunlight. Overall, this study improves our understanding of the optical mechanisms responsible for the silver color of C. bombycina and the remarkable thermoregulatory properties of the hair coat covering the ant's body.