The discharge of urban stormwater may cause a sudden temperature increase in receiving waters that may be harmful to fish and other aquatic organisms. A screening procedure is proposed with temperature thresholds for the runoff from roofs and roads as well as for the receiving water system to protect brown trout from thermal damage. The stormwater temperature is calculated on the basis of a simple thermodynamic estimate for different latitudes. Only receiving waters with maximum daily mean temperatures of 22 °C (T1) are considered potential habitats for brown trout. The maximum temperature for a 1-h exposure time with a safety margin for 100% survival is 25 °C (T2), the sudden temperature change at the beginning of a rain event must not exceed 7 °C (T3), and fish-egg development requires the daily maximum temperature in winter to be below 12 °C (T4). Examples of stormwater runoff from roof or road surfaces from Switzerland validate our approach within ±0.5 °C. Effects of runoff into receiving waters without detailed data can be predicted within ±0.8 °C. With the restriction by T1, T2 seems not to be an acute problem at Swiss latitudes. T3 could play a role, especially if a large amount of runoff is discharged in small and rather cool rivers and streams. Finally, T4 deserves more attention than hitherto given. The proposed procedure may be a useful tool for assessing the influence of urban stormwater on the temperature of the receiving waters, particularly with regard to predicting the thermal impacts of urban or suburban runoff to populations of brown trout.