A two-dimensional particle-based heat transfer model is used to train a deep neural network. The latter provides a highly efficient surrogate that can be used in standard inversion methods, such as grid search algorithms. The resulting inversion strategy is utilized to infer statistical properties of fracture networks (fracture density and fractal dimension) from synthetic thermal experimental data. The (to-be-estimated) fracture density is well constrained by this method, whereas the fractal dimension is harder to determine and requires adding prior information on the fracture network connectivity. The method is tested on several fracture networks and hydraulic conditions.