The combined heat and power system is a highly efficient energy source for many applications because heat and power are often of high demand. Although fuel cells and thermoelectric generators are popularly known to be used separately for combined heat and power purposes, there is little research on combining these two components for this application. This research proposes to analyze the hybrid fuel cell and thermoelectric system specifically when it is used as a combined heat and power system - thus forming a newly proposed fuel cell and thermoelectric combined heat and power (FC-TE-CHP) system. The key idea is to use the thermoelectric device to further improve the exergetic and temperature performance of the conventional fuel cell based combined heat and power (FC-CHP) system. Both systems are analyzed and compared by using a steady state thermodynamic model from both the temperature and exergetic perspectives. The exergetic efficiency and temperature results are reported by performing parametric sweeps of several key parameters such as fuel cell stack electric power, operation in thermoelectric cooler mode, water mass flow rate and radiator air convection coefficient. Subsequently, recommendations on how the FC-TE-CHP system can be operated efficiently in terms of exergy are drawn.