This paper reports work in which molecular dynamics are used to simulate a single cascade of a quantum cascade laser diode with the intent of computing the effective thermal conductivity in the cross-plane direction. The Tersoff potential is used with coefficients found from the literature for inter-atomic forces, and the Green-Kubo relation is 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.