Surface air temperature is critical for understanding the energy-mass balances of mountainous regions and evaluating the representation of the water cycle in atmospheric models. Furthermore, estimates of extremely warm temperatures are needed to fully anticipate resulting impacts on pre-existing snowpack, such as rapid ablation and downstream effects on water resource management and infrastructure. Accurate quantification of the geospatial distribution of surface air temperature in mountains remains a scientific grand-challenge. To meet these needs, gridded data products use various statistical methods to translate irregularly sampled in situ measurements to estimates of temperature on regular space-time units. However, in mountain regions, the placement of monitoring stations may not accurately represent the heterogeneity of temperature. This means that simple interpolation schemes can introduce errors and uncertainties into the resulting gridded estimates and are often not provided. Here, we show how probabilistic, extreme-aware gridding methods such as Gaussian processes (GPs) provide an improved characterization of daily maximum temperature in mountainous terrain. Using the Southern Rocky Mountain range as an illustrative example, we find that GP-based gridding systematically reduces out-of-sample prediction errors for both bulk statistics and high percentiles of surface air temperature while providing explicit estimates of uncertainty through an ensemble, rather than a more traditional deterministic approach. This improved performance is due to explicitly accounting for multiple-day autocorrelation innate to temperature records and known relationships between daily temperature and its co-variates (e.g., elevation, solar radiation, and topographic variability).