The paper presents a mathematical model developed to simply analyze a hybrid hollow-core-floor-slab-wall-air-collector system with passive discharge to the rooms above and below the slab. It is based on a one-dimensional (longitudinal) detailed thermal analysis of the basic module, that is comprised of two parts (one along the cores with incoming air, and the other along those with outgoing air). The model accounts, in addition to the exact heat exchange along the module, for transverse heat exchange between the two parts within the module, transverse hear exchange with the adjacent modules, and heat exchange with the surrounding air at every point along the system. It incorporates thus the relevant heat transfer mechanisms associated with all the physical factors of the system that require optimization, while avoiding the time consuming complete 3-D thermal analysis required for a thorough and totally accurate analysis. The field equations consist of four second order partial differential equations, with four unknowns, at every point along the system. The numerical solution was accomplished by means of a finite difference scheme, that yielded a banded coefficients matrix. The integration was performed for Ih time steps by means of a computer program (DEKOLTA-Decke-Kollektor-Thermal-Analysis) developed specifically for the purpose. In order to illustrate the application of the procedure for thermal performance analysis of a hybrid system the paper presents results for three case studies of a system with two different rooms along the slab.