We propose a methodology combining physical modelling and machine learning (ML) to estimate the apparent ground thermal diffusivity at the scale of a country. Based on ground temperature time series at different depths, we estimate the diffusivity at 49 Swiss stations using Fourier analysis. Using a geology database, the diffusivity estimations are cross-validated with typical values for common rocks. Random Forests, an ML algorithm, are used to train a model using the previous diffusivity estimations as output values and multiple geological, elevation and temperature features. The model, showing a testing error of 16.5%, is then used to perform the estimation of apparent diffusivity everywhere in Switzerland.