In Tunisia, the building sector is considered as a major issue of energy consumption. A special attention should be drawn to improve the thermal quality of the building envelope with real consideration of the Tunisian climate specificity. One of the most effective measures is the roof insulation. Therefore, the present study is concerned with the determination of the optimum insulation thickness and the resulting energy savings and payback period for two typical roof structures and two types of insulation materials. An efficient analytical dynamic model based on the Complex Finite Fourier Transform (CFFT) is proposed and validated in order to handle the nonlinear longwave radiation (LWR) exchange with the sky. This model provides a short computational time solution of the transient heat transfer through multilayer roofs, which could be a good alternative to some numerical methods. Both heating and cooling annual loads are rigorously estimated and used as inputs to a life-cycle cost analysis. Among the studied cases, the most economical one is the hollow terracotta-based roof insulated with rock wool, where the optimum insulation thickness is estimated to be 7.9 cm, with a payback period of 6.06 years and energy savings up to 58.06% of the cost of energy consumed without insulation. The impact of the LWR exchange component is quantified and the results show its important effect on the annual transmission loads and, consequently, on optimum insulation thickness. A sensitivity analysis shows the efficiency of cool roofs in the Tunisian climate context, where the cooling energy cost benefits outweigh the wintertime penalty. Comparison of CFFT results with those of sol-air Degree-Hours (DH) shows that optimum insulation thickness and energy savings are overestimated and payback period is underestimated using the latter model. The proposed CFFT model could be an efficient tool for the design and the energy analysis of building envelope components in various climatic locations. (C) 2016 Elsevier Ltd. All rights reserved.