Currently, the development of small-scale power and heat generation technologies, capable of utilizing locally available low-grade biomass resources, appears to be a reasonable pathway to secure energy supply and meet the green energy goals. An externally-fired gas turbine cogeneration system, operated under the Brayton cycle with air as the working fluid, even though it involves some technical challenges, offers a relatively simple design, as well as manageable and safe operating conditions. Furthermore, along with its fuel flexibility and supportive role in energy supply stability, it is considered to be economically viable compared to other more advanced renewable-based technologies. Furthermore, owing to its fuel flexibility and its potential to support energy supply stability, the system may also represent an economically competitive option among small-scale renewable energy technologies. Such a solution, thus, seems to be a promising option, particularly for regions with abundant raw biogenic resources. The present study focuses on the concept of a solid biomass-fueled cogeneration plant operated under the regenerative Brayton cycle with an electrical power output of approximately 100 kW, which addresses the typical energy needs in rural areas. The system comprises an air compressor, turbine, high-temperature heat exchanger (air preheater), combustion chamber and a utility heat exchanger. The high-temperature heat exchanger is a key component of the cycle, as it determines the maximum temperature of the generated flue gases, which translates into the efficiency of the system. Thus, the study carried out involves the analysis of a high-temperature heat exchanger performance and sizing in terms of a trade-off between maximizing system efficiency and technical constraints and cost-effectiveness. The thermodynamic calculations solve the system of thermodynamic and heat transfer equations for individual components, while utilising the RefProp database to determine variable properties of the fluids. The isentropic efficiencies of the compressor and the turbine are taken into account. The profitability of the system is examined and discussed through the analysis of economic indicators such as capital expenditure, operating expenses and the payback period. The study provides a basis for identifying operating and design conditions under which externally fired Brayton cycle units may become a viable solution for small-scale biomass-based cogeneration.