In this work, a discontinuous Galerkin finite element method, for a discontinuous transmission problem, is proposed to model the thermal wave scattering in lock-in thermographic inspection of cracked opaque samples with general inner cracks. Unlike continuous finite element methods, the model we present does not require meshing of the gaps within the cracks, radically reducing the amount of degrees of freedom and the elapsed time spent during the simulation. We will focus on analyzing the sensitivity of the temperature propagation through the crack under different parameters such as length, depth, thermal resistance of finite cracks and parameters involving the modulated laser excitation.