One-dimensional thermodynamic model of the hybrid direct carbon fuel cell (HDCFC) is developed. A full process of electrochemical oxidation of carbon is considered as a sequence of injections of oxygen from the parallel air duct into carbon/carbonate slurry. Equilibrium composition of the mixture C+CO+CO₂ is assumed to be established in the anode compartment after each oxygen injection. As a result of modeling the hybrid direct carbon fuel cell turns out to be a gasifier cell (GC), almost completely converting carbon to carbon monoxide, generating electricity with thermodynamic efficiency greater than 1, doing this at the expense of heat intake. Combined with solid oxide fuel cell (SOFC), using CO as a fuel, in one energy conversion plant, GC provides an inimitable efficiency of conversion of chemical energy into electricity (up to 86%) due to the unique situation, when GC uses the heat, generated by SOFC.