A generalized analytical framework based on the Distributed Transfer Function Method is developed for one-dimensional transient heat conduction in multilayer walls with imperfect thermal interfaces. The formulation accounts for layer-dependent thermophysical properties, prescribed thermal contact conductance, interfacial temperature jumps, and time-dependent convective and solar boundary conditions. To accommodate measured environmental excitations that are not globally differentiable, an adaptive temporal-segmentation strategy is introduced. Outdoor-air temperature and incident solar heat flux measured in Gaziantep, Turkey, are represented by piecewise Gaussian and sinusoidal regressions over analytically tractable intervals, with the terminal temperature field of each segment transferred as the initial condition of the next. Six three- and five-layer wall configurations, W1-W6, are analyzed with room air maintained at 25 °C. The analytical predictions are verified against an independent conservative finite-difference formulation using layer-conforming grids, duplicated one-sided interface nodes, direct contact coupling, and fully implicit backward Euler integration. Grid- and time-step-independence studies are performed for all configurations. Close agreement is obtained for temperature distributions, interfacial temperature jumps, and room-side heat fluxes, with a maximum temperature difference of 1.06 °C at the evaluated locations. Room-side heat fluxes are separated into heating and cooling contributions and integrated over 24 h to estimate air-conditioning electricity consumption. W5, containing extruded polystyrene insulation, exhibits the lowest total consumption (0.15546 kWh), followed by W6 (0.161744 kWh). Among the three-layer walls, W2 gives the lowest total consumption (0.273031 kWh). The results show that energy performance depends on insulation, wall thickness, thermal storage, layer arrangement, heating-cooling balance, and interfacial thermal resistance.