Turbulent energy flux is an important unclosed term in the mean energy conservation equation. It is conventionally modelled using gradient diffusion hypothesis in terms of turbulent conductivity and gradient of mean temperature. However, in the region of shock, this hypothesis leads to unrealistic predictions of turbulent energy flux in turn over-predicting the wall heat flux values as seen in most RANS results. An important unclosed term in momentum conservation equation is Reynolds stress which is also conventionally modelled using gradient diffusion hypothesis in terms of eddy viscosity and gradient of mean velocity. The over-prediction of Reynolds stress in the shock region is curbed by using the realizability constraint formulation which applies a constraint on the eddy viscosity such that Reynolds stress is limited. In this work, we apply the realizability constraint to turbulent energy flux and see its potential in curbing the peak values in the region of shock.