We propose a chemo-thermal model that considers both diffusion and reaction phenomena, consumption and formation of species, and heat generation due to chemical reactions. We study the thermal and chemical processes in combustion of heterogeneous reactive materials at the microstructural level. The model is applied to the combustion of Nickel and Aluminum (Ni/Al) composites. We provide numerical results such as the reaction front speed, reaction time, and temperature evolution during reaction and compare those with the existing experimental data. Sensitivity analysis and Bayesian calibration of the diffusion and reaction parameters are performed. We show that both diffusion and reaction are strongly coupled in thin zones such that neither can be neglected. Moreover, a multi-fidelity and multi-scale Gaussian process emulator is developed to overcome the computational cost of the simulations at different length-scales. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.