Climate change leads to an overall increase of heatwaves in many countries, and this can lead to risks for the health, and specifically for housing building occupants. Public policies about overheating risk mitigation in buildings have to be implemented and should rely on a precise and exhaustive description of the initial state of the building capacity to mitigate overheating. This paper presents a methodology used to calculate an overheating indicator for each housing at a country scale (around 20 million housing buildings). Because the model developed to calculate this overheating indicator must be fast enough to be applied on 20 million buildings, without giving up on the accuracy of detailed simulation models, a machine learning approach has been chosen. The overheating indicator was first calculated on a large sample of housing buildings using dynamic thermal simulation. The results of these simulations enabled to identify the housing most influential parameters on overheating: its geometry, inertia, windows size, and the insulation of its walls and roof. Then, a random forest regressor was trained to provide an accurate statistical model with almost instant computing performance. As a result, we could evaluate the overheating indicator for all the 20 million housings in France providing much information about population health risks.