A mathematical model for a thermoelectric generator (TEG) based on constitutive equations has been developed to analyze temperature dependent performance in terms of output power and efficiency. Temperature dependent material properties and thermal losses, which occur as conductive and radiative heat transfer, were considered in the finite element model. Effective material properties were invoked for understanding the influence of temperature dependence of material parameters and related adverse effects on the model TEG. It is shown that analytical equations with effective properties can provide excellent estimation of the performance of a TEG over a broad operating range. The model was simulated, analyzed and validated to examine the effects of different operating conditions and geometry that interact with thermal losses inside the TEG. We believe that this model will further expedite the optimization of TEGs being developed using new material compositions.