A strategy is proposed for the design of wall envelopes to improve unsteady thermal performance in non-air-conditioned buildings and to reduce energy costs in air-conditioned buildings. The thermophysical properties of building materials (e.g., burnt bricks, mud bricks, laterite stone, cinder concrete, and expanded polystyrene) were measured experimentally using a thermal analyzer. A total of 28 combinations for composite walls were designed with expanded polystyrene as an insulation material based on seven criteria and were subjected to 8 different external surface heat transfer coefficients, which were tested for unsteady thermal performance parameters and air-conditioning cost-saving potential. In this paper, unsteady thermal transmittance obtained from admittance method has been employed to compute cost saving potential of air-conditioning for the various wall envelopes. The use of C–H5 design at a 2 m/s wind speed was found to increase the decrement lag of burnt brick, mud brick, laterite stone, and cinder concrete composite wall envelopes by 48.1%, 49.0%, 59.5%, and 47.0%, respectively, relative to the common wall design (C–H1) in non-air-conditioned buildings. The laterite with a C–H5 design offers the highest annual energy cost savings (1.71 $/m2 at 2 m/s), the highest life cycle cost savings (18.32 $/m2 at 2 m/s), and the lowest payback period (4.03 yrs at 2 m/s) in all tested building materials for air-conditioned buildings. The overall results of this study are expected to open new paths to deliver simple design strategies for energy-efficient buildings. © 2020 Elsevier Inc.