By integrating an Absorption Refrigerator (AR), a new hybrid system model is established to reuse the waste heat from a Molten Carbonate Direct Carbon Fuel Cell (MCDCFC) for additional cooling production. Various irreversible losses in each element of the system are numerically described. The operating current density span of the MCDCFC that allows the AR to work is derived. Under different operating conditions, the mathematical expressions for equivalently evaluating the hybrid system performance are derived. In comparison with the stand-alone MCDCFC, the maximum attainable power density of the proposed system and its corresponding efficiency are increased by 5.8% and 6.8%, respectively. The generic performance features and optimum operating regions of the proposed system are demonstrated. A number of sensitivity analyses are performed to study the dependences of the proposed system performance on some physical parameters and operating conditions such as operating temperature, operating current density, and pressure of the MCDCFC, cyclic working fluid internal irreversibility inside the AR, thermodynamic losses related parameters and the anode thickness of the MCDCFC. The obtained results may offer some new insights into the performance improvement of an MCDCFC through a reasonable heat management methodology.