In this paper, the overall effective thermo-mechanical properties of limestone samples are estimated using a micro–macro mechanical approach. A mathematical framework is proposed to estimate the overall properties based on local geometrical considerations using Mori–Tanaka’s scheme. In addition, a homogenization-based mathematical formulation is proposed to predict the effective thermal conductivity of composite materials subjected to periodic micro-scale heat fluxes and governed by Fourier’s law and steady state balance equations. Moreover, Coussy’s approach is used to derive the expression of heat capacity. In order to take into account the degradation of heterogeneous rock materials, a damage based numerical model that uses the homogenized thermo-mechanical properties and Griffith’s criterion is proposed. The model is implemented as an external user material subroutine to the multi-purpose finite element software Abaqus, to assess the damage of a limestone rock sample under normal percussion drilling conditions. Moreover, a model parameter identification procedure is performed to calibrate the necessary parameters using a simple indentation test. The obtained results show that the numerical model can reproduce the elastic damaged behavior of rocks, such as limestone, subjected to a simple indentation that mimic the conditions of rock drilling. Finally, the proposed analysis proves that effect of temperature on the overall behavior of limestone can be investigated using multi-physics upscaling.