In this paper, we consider the transient state behavior of a segmented thermoelectric generator (STEG) exposed to a variable heat input power on the hot side while the transfer of heat on the cold side is by natural convection. Numerical analysis is used to calculate the power generation of the system. A one-dimensional STEG model, which includes Joule heating, the Peltier effect with constant properties of materials, is considered and governing equations are solved using the finite differences method. The transient analysis of this model is typical for energy harvesting applications. A novel design methodology, formulated on the ratio of the figure of merit of the thermoelectric materials, is developed including segmentation on the legs of the thermoelectric generator, which does not consider previous studies. In our approach, the figure of merit is an advantageous parameter to analyze its impact on thermal and electrical efficiency. The transient state of the thermoelectric generator is analyzed, considering two and three heat input sources. We obtain the temperature profiles, voltage generation, and efficiency of the STEG under pulsed heat input power. The results showed that the temperature drop along the semiconductor elements was more considerable when three pulses were applied, and when the thermal conductivity in the first segment was higher than that of the second segment. Furthermore, we show that the generated voltage and the maximum efficiency in the system occur when the value of the figure of merit in the first segment, which is in contact with the temperature source, is lower than the figure of merit for the second thermoelectric segment of the leg. The model investigated in this paper offers an essential guide on the thermal and electrical performance behavior of the system under transient conditions, which are present in many variable thermal phenomena such as solar radiation and the normalized driving cycles of an automotive thermoelectric generator.