The study presents a concept and calculations concerning the operation of the direct carbon fuel cell (DCFC) with molten hydroxide electrolyte (MH-DCFC) as the basic source of electricity integrated with heat and cool air generation systems. The technology of direct carbon fuel cells assumes the direct use of a carbon fuel (such as fossil coal, carbonized biomass, graphite, coke etc.) to generate electricity with high efficiency and low impact on the environment. These cells operate by utilizing carbon fuel in the range of temperatures of 673–973 K and allow for generation of electricity with an efficiency of about 56%. In order to improve the fuel conversion efficiency, the heat generated in the process of cell cooling can be used to prepare hot water, for heating during the heating season, while during the summer period, heat from cooling of the direct carbon fuel cells can be utilized in the process of cool air production (chilled air) using absorption chillers for e.g. air conditioning. This paper presents a case study and simulation calculations of the system composed of MH-DCFC that generates electricity, and runs heat exchangers and an absorption chiller, integrated with the fuel cell to generate heating and cooling for improving the efficiency of the whole system. The maximum heat and cool streams that can be obtained during the operation of the cell were also evaluated. The results obtained in the study can be helpful in the design of autonomous buildings equipped in direct carbon fuel cells as sources of electricity integrated with the systems of heat and cool generation.