We reconstruct the CDM model for Theory, where is the torsion scalar and the trace of the energy-momentum tensor. The result shows that the action of CDM is a combination of a linear term, a constant () and a non-linear term given by the product $\sqrt{-T}F_g\left[(T^{1/3}/16\pi G)\left(16\pi G\mathcal{T}+T+8\Lambda\right)\right]$, with being a generic function. We show that to maintain conservation of energy-momentum tensor should impose that must be linear on the trace . This reconstruction decays in the Theory for , with a constant. Our reconstruction describes the cosmological eras to the present time. The model present stability within the geometric and matter perturbations for the choice , where , except for geometric part to de Sitter model. We impose the first and second laws of thermodynamics to the CDM and find the condition where they are satisfied, that is, , however where this is not possible for cases where we choose, leading to a breakdown of positive entropy and Misner-Sharp energy.