Uncontrolled solar radiation and the related effects on occupant productivity can lead to considerable indoor thermal discomfort in office environments. In this paper, the Radiance Daylight Coefficient (DC) method is used to assess incoming solar radiation and consequent indoor thermal discomfort through delta mean radiant temperature (ΔMRT). The ΔMRT allows expressing an adjusted predicted mean vote (Adjusted PMV). Under the conditions of direct solar radiation, the Adjusted PMV value surpasses the applicability range of the standard PMV in terms of MRT value. To overcome this limitation, the assessment of the effect of incoming shortwave solar radiation is expressed in the heat stress index of wet bulb globe temperature (WBGT). This procedure was tested under a variety of climatic conditions (e.g., Sol-air temperature) to estimate dissatisfaction in indoor office environments located in Milan (Italy) for an occupant positioned at different distances from the fenestration (0.75 m, 1.25 m, and 1.75 m) and exposed to direct solar radiation (e.g., without shading devices). The condition with no shading device was then compared with the condition with shaded glazing to test the impact of the solar radiation on the indoor thermal stress conditions. The results reported through ΔWBGT allow the estimation of the heat stress conditions on an annual basis when ΔWBGT > 0. Finally, it is proposed that the metric of Annual Radiation Heat Stress (ARHS) should include ΔWBGT and assess the heat stress spatially due to the incoming direct solar radiation.