The results of a numerical analysis of unsteady heat transfer in the "metal-mold-environment" system during continuous combined casting and extrusion of an aluminum alloy in an installation with a horizontal carousel mold are presented. The heat engineering zones characterized by different intensity of heat transfer between the melt and the surface of the mold have been determined. A quantitative assessment of the influence of the rate of heating of the crystallizer on the temperature-time characteristics during the period of the transient thermal process is given. It is shown that an increase in the productivity of the installation reduces the duration of the transient thermal process when starting the installation from a cold state until it reaches a stationary thermal regime. The dependence of the time at which the installation reaches the stationary thermal regime on the rotation speed of the crystallizer wheel has been obtained.