Thermoelectric energy conversion is perhaps the most promising of the potential applications of molecular electronics. Ultimately, it is desirable for this technology to operate at around room temperature, and it is therefore important to consider the role of dissipative effects in these conditions. Here, we develop a theory of thermoelectricity which accounts for the vibrational coupling within the framework of the Marcus theory. We demonstrate that the inclusion of lifetime broadening is necessary in the theoretical description of this phenomenon. We further show that the Seebeck coefficient and the power factor decrease with increasing reorganization energy and identify the optimal operating conditions in the case of non-zero reorganization energy. Finally, with the aid of density functional theory calculations, we consider a prototypical fullerene-based molecular junction. We estimate the maximum power factor that can be obtained in this system and confirm that C60 is an excellent candidate for thermoelectric heat-to-energy conversion. This work provides general guidance that should be followed in order to achieve high-efficiency molecular thermoelectric materials.