A numerical model is presented for investigating control of the three-dimensional boundary-layer transition process. Control of a periodically forced, spatially evolving boundary layer in water is studied using surface heating techniques. The Navier–Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. The Navier–Stokes equations are used in vorticity–velocity form and are coupled with the energy equation through the viscosity dependence on temperature. Passive control of small amplitude two-dimensional waves and three-dimensional oblique waves is numerically simulated with either uniform or non-uniform wall heating applied. Both amplitude levels and amplification rates are strongly reduced with heating applied. Comparison is made with parallel and non-parallel linear stability theory and experiments. Control of the early stages of the nonlinear breakdown process is also investigated using uniform wall heating. Both control of the fundamental and subharmonic routes to turbulence are investigated. For both breakdown processes, a strong reduction in amplitude levels and growth rates results. In particular, the high three-dimensional growth rates that are characteristic of the secondary instability process are significantly reduced below the uncontrolled levels.