By using molecular dynamics technique, we have computed the effective cross-plane thermal conductivity of a single cascade of a quantum cascade laser diode. Additionally, the local phonon density of states was also computed. The Tersoff potential was used with coefficients found from the literature for inter-Atomic forces, and the Green-Kubo relation was used to compute the conductivity from the integral of the system heat flux autocorrelation. The computed conductivity lies in the same range as measurements found in the literature, but the local density of states deviated from expected values based on local diode composition, suggesting that previous assumptions made about electron-phonon coupling are incorrect.