With the current environmental issues and climatic change, it is of major importance to design highly energy efficient buildings. Several programs have been developed in the past 50 years to model the transfer phenomena in building enclosure to assess the global energy consumption. However, the enclosures are always designed as plane by association of several layers of different properties. In other words, is it not possible to design enclosures with shapes and topology optimized to minimized the transfer? The issue of the project is to develop a numerical and experimental framework to advanced design of building enclosures with optimized shape and topology. The answer to this considerable issue relies in tackling the lack of the actual state-of-the art models and experimental facilities. A combined experimental-modelling approach will be developed: (1) an innovative model with transient transfer processes considering time and space varying boundary conditions (2) elaborating a fast optimization numerical strategy to retrieve the varying topology and shape of enclosures and (3) verifying the insights with a pioneering experimental demonstrator based on 3D printing and controlled facility.