The release of airborne hazardous substances in the urban roughness sublayer (RSL) is a risk to human health. The atmospheric dispersion of these materials should be contained to mitigate their adverse consequences. This study investigates the effects of atmospheric stability on the air, heat, and pollutant transport within RSL by a validated 3-D RANS code. A building morphology with height variance is proposed for better representing the real urban environment and characterizing the complex interactions between the roughness elements and the flow regimes. The thermal stratification stability test subject to the ground-inflow temperature difference is extended to span from strongly unstable to moderately stable. The quantitative indicators, including air exchange rate, heat removal rate, pollutant removal rate, heat transfer coefficient, and pollutant transfer coefficient, are introduced and analyzed. The correlations between indicators and thermal stabilities are established, which provides explicit expressions to describe the influence of the changing bulk Richardson number (Rb). Results show that the design of height-variance elements enables a stronger lateral momentum towards the target street canyon, which suppresses the spanwise dispersion of pollutants. The discussions upon heat and pollutant transport based on stability categories show a high Rb-dependence of heat/mass transfer efficiency. The stability threshold is demonstrated to be Rb ≈ 0.7, where the flow speed near the ground approaches zero. As a result, the high temperature gradient is formed and acts as positive feedback to facilitate a more stratified condition. The accurate and rational correlations obtained in this study will save the computational cost considerably for further research. Also, the available results will be a reference for environmentally friendly designs.