The primary focus of this article is to capture heterogeneous treatment effects measured by the conditional average treatment effect. A model averaging estimation scheme is proposed with multiple candidate linear regression models under heteroskedastic errors, and the properties of this scheme are explored analytically. First, it is shown that our proposal is asymptotically optimal in the sense of achieving the lowest possible squared error. Second, the convergence of the weights determined by our proposal is provided when at least one of the candidate models is correctly specified. Simulation results in comparison with several related existing methods favor our proposed method. The method is applied to a dataset from a labor skills training program.