A downhole burner for a steam generator includes an injector and a cooling liner. Steam enters the burner through holes in the cooling liner. Combustion occurring within the cooling liner heats the steam and increases its quality and may superheat it. The heated, high-quality steam and combustion products exit the burner and enter an oil-bearing formation to upgrade and improve the mobility of heavy crude oils held in the formation. The injector includes a face plate, a cover plate, an oxidizer distribution manifold plate, and a fuel distribution manifold plate. The cooling liner has an effusion cooling section and effusion cooling and jet mixing section. The effusion cooling section includes effusion holes for injecting steam along the cooling liner surface to protect the liner. The effusion cooling and jet mixing section has both effusion holes and mixing holes for injecting steam further toward central portions of the burner.