Water temperature is a hydrological factor which affects the habitat suitability of many aquatic (fish) species, and is therefore of great concern in the actual context of climate change. Two types of models are currently used to simulate stream temperature: physically-based models, which are typically applied only over limited areas, and regression models, which usually lack the ability to make predictions in ungauged areas. As an attempt to bridge the gap between these two types, we propose a hybrid model based on the energy-balance equation, in which the terms are related to catchment physiographic variables via empirical relationships. The physiographic variables are chosen so as to be available over the entire country (Switzerland), enabling the model to be used in ungauged catchments. This approach is on the one hand more physically-based than the usual regression models – hereby limiting the degree of empiricism associated with its derivation – but on the other hand seeks simplicity and applicability over large areas – making it more practical than the usual physically-based models. In order to test this model, we use it to predict the monthly mean stream temperature over 23 selected medium-sized catchments (3–300 km2) in Switzerland. While selecting the catchments, particular attention is given to cover a large range of different geomorphological conditions, especially regarding altitude, slope and aspect. It is shown that the model compares favorably with standard empirical models such as multi-linear regression.