In this paper, we propose an extension of the amalgam method to reduce advection diffusion problem with time dependent parameters. From a full general basis, this technique consists to select rapidly the most influent modes, and to add to them the remaining modes balanced by a coefficient. The originality of this paper lies in the fast obtention of a full degraded model, used as a reference in a minimization process of the reduced model's error. Transcribed to the physical space, this error approaches the error between the reduced model and the real physical finite elements model. The treated application is a disk rotating at a variable velocity with time dependent thermal inputs. Comparison between the reduced and the finite elements model gives a gain in term of computational time of 36 for a mean error on the entire domain equal to 0.42%. (C) 2011 Elsevier Ltd. All rights reserved.