The power factor of a thermoelectric device is a measure of the heat-to-energy conversion efficiency in nanoscopic devices. Yet, even as interest in low-dimensional thermoelectric materials has increased, experimental research on what influences the power factor in these systems is scarce. Here, we present a detailed thermoelectric study of graphene quantum dot devices. We show that spin degeneracy of the quantum dot states has a significant impact on the zero-bias conductance of the device and leads to an increase of the power factor. Conversely, we demonstrate that nonideal heat exchange within the leads can suppress the power factor near the charge degeneracy point and nontrivially influences its temperature dependence.