In this paper, rate dependent evolution laws are identified and characterized to model the mechanical (elasticity-based) and thermal damage occurring in coarse grain refractory material subject to cyclic thermal shock. The interacting mechanisms for elastic deformation driven damage induced by temperature gradients and thermal damage induced by isotropic thermal expansion are combined and represented by a single variable for the total damage. The constitutive model includes the shielding of micro-structural thermal damage by the non-local elasticity-based damage developed at the macroscopic and microscopic scale. Quasi-stationary thermal experiments are used to identify the parameters used in the evolution law for thermal damage. The remaining model parameters, including a micro-structural length scale, are quantified by inverse modelling of cyclic thermal shock experiments. Longitudinal wave propagation measurements through damaged material are simulated, enabling the identification on the basis of the first and second thermal shock cycle. A third thermal shock cycle enabled the evaluation of the quality of the obtained parameter set. The set-up of the thermal shock experiments has been optimized through a parameter identifiability analysis. The damage evolution in three consecutive thermal shock cycles is investigated numerically with the optimized model.