1. Ambient temperatures in natural environments can vary widely over short distances, especially on rugged ground where exposure to solar radiation depends on slope and aspect. Temperatures can also fluctuate rapidly, reaching values not revealed by climate data. Such fine-scale variation raises challenges for modelling species distributions under changing climates. 2. To avoid misunderstanding current species distributions and future changes, temperatures must be modelled at high resolutions. Most existing methods either require extensive parameterisation or are pre-parameterised for restricted localities and current conditions; here we describe a more versatile method intended for European landscapes under a wide range of scenarios. 3. The availability of high-resolution topographic data makes possible the use of projected solar irradiation to help predict local diurnal ground temperatures. Using time series from 83 points across Europe, we fitted statistical models for soil surface temperature based on geographical characteristics of the sites along with atmospheric variables obtained from a publicly-available database. The sites ranged from 40°N to 60°N and 2°W to 25°E, and from 43m to 1500m in elevation. 4. We compare models for monthly mean and daily afternoon temperatures, for open and tree-covered habitats. The effect of topography was greatest for the daily predictions, and generally more important in open than in tree-covered sites. Tests with data collected from other European locations in a different time period suggest that our models can predict monthly means with an error standard deviation of 2.7°C. We provide an R function that implements our models on the basis of readily-available data. 5. Our mean-temperatures model should be useful for understanding organisms’ niches, dispersal possibilities and community dynamics, and for predicting species’ refugia, range shifts and opportunities for adaptation under projected climate change.