International audience Methods of interpolation, whether based on regressions or on kriging, are global methods in which all the available data for a given study area are used. But the quality of results is affected when the study area is spatially very heterogeneous. To overcome this difficulty, a method of local interpolation is proposed and tested here with temperature in France. Starting from a set of weather stations spread across the country and digitized as 250 m-sided cells, the method consists in modelling local spatial variations in temperature by considering each point of the grid and the n weather stations that are its nearest neighbours. The procedure entails a series of steps: recognition of the n stations closest to the cell to be evaluated and subdivision of the study area into polygons defined by a neighbourhood rule, elaboration of a local model by multiple regression for each polygon, and application of the parameter estimate from the regression to obtain a predicted value of temperature at each point of the polygon under consideration. These results are compared with results from three global interpolation methods: (1) regression, (2) ordinary kriging, and (3) regression with kriging of residuals. We then develop the original results from local interpolation such as mapping of the coefficients of determination and of the parameter estimate related to altitude and to distance to the sea. These developments highlight the processes that dictate the spatial variation of climate