Climate responsive building design involves the study of the thermal response of building and insulating materials exposed to periodic changes of environmental conditions. For calculation of such unsteady thermal characteristics, one dimensional heat flow diffusion equation under periodic boundary conditions was solved using matrix algebra and thermal characteristics like admittance, transmittance, decrement factor, time lag, surface factor and surface factor time lags were calculated for homogeneous and composite walls. In this study, ten building and ten insulating materials were studied. Optimum wall thicknesses of building and insulating materials were calculated. From the results, it was concluded that mud phuska and coconut pitch are the most recommended homogeneous building and insulation materials respectively, among studied building and insulating materials, from lower decrement factor and higher time lag point of view. It is found that the insulation materials are highly responsive to short wave radiation than that of building materials. From the study, ultimately it is concluded that Burnt brick composite walls with Coconut pitch insulation is the best composite wall among all studied walls for reduced cooling loads and the most energy efficient building construction. © 2014 30th International PLEA Conference: Sustainable Habitat for Developing Societies: Choosing the Way Forward - Proceedings. All rights reserved.