The present work focuses on analyzing the effect of building envelope configuration on thermal response parameters (TL and DF) and cooling load in the composite climate of India. Two major cities of the composite climate (Raipur and New Delhi) are chosen and five different envelope configurations are tested. A numerical model is developed to analyze heat transfer through building envelope and its thermal response. The model is validated with the experimental results available in the literature and also with the experiments conducted in one of the cities (Raipur). Further, simulations have been carried out to predict cooling load, time lag (TL) and decrement factor (DF) of various envelope configurations for the composite climate. It is observed that effect of TL and DF is significant in addition to U-value (thermal transmittance). Envelope which possesses higher TL value and lower DF is preferable as it yields lower cooling load. Moreover, it is observed that the insulation provided by the building envelope is sensitive to the location while considering the combined effect of solar radiation and outside air temperature.