Field-scale properties of fractured rocks play crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross-borehole thermal experiments data. It is based on a particle-based heat-transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of heat-transfer model runs, and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to-be-estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding non-uniform prior information related to the DFN connectivity improves the inference of this parameter.