In this letter, we consider the question of designing insulator/metal thermovoltaic structures with periodically corrugated interfaces that give optimal performance based on the metric of useful power density. Using a Monte Carlo approach in a robust, rapid, and high-accuracy numerical simulation strategy, we have identified such interface shapes. We searched among the class of sinusoids and found that a flat-interface configuration could be significantly improved in transverse magnetic polarization. More specifically, we found that (i) the performance improves with increasing corrugation amplitude (ii) up to a maximum, (iii) the shape of the corrugation is largely irrelevant, and (iv) the period of the corrugation should be chosen in connection to the bandgap energy of the photovoltaic cell. For the latter, we provide a simple expression as a starting point for practitioners interested in fabricating such structures.