In this paper, the thermo-optical performance using novel cooling strategy improvements for a hybrid photovoltaic/parabolic dish concentrator with a conical thermal receiver using a beam splitter filter (PV/PDC-CTR-BSF) is investigated. The study’s main goal is to improve the cooling effectiveness of the serpentine-shaped cooling duct by investigating the effect of the cross-section shape and positioning of the cooling duct under the PV panel. Typical cooling pipes have either a rectangular or circular cross-section and are usually attached to the back sheet of the PV panel using off-the-shelf adhesives that have very low thermal conductivity. With the advent of 3D printing technology, the back sheets could be 3D-printed with integral cooling ducts of different cross-sections at different locations and orientations within the back sheet that allow for increased heat transfer from the back sheet and thus improve PV/PDC-CTR-BSF’s thermos-optical performance. For this purpose, the study investigates and compares the thermal performance of four different cooling duct cross-sections that include: rectangular, semi-circular, semi-elliptical and triangular. For each of the cooling duct cross-sections, several positions and orientations, which include flush below the back sheet layer and embedded inside the back sheet but positioned at the bottom, middle and top of the back sheet, are examined. Numerical simulations using the commercial software ANSYS FLUENT(R2019) are performed to assess the performance of the cooling ducts and, in turn, the thermo-optical performance of the PV/PDC-CTR-BSF system. The semi-elliptical cross-section duct embedded in the middle of the back sheet was found to yield the best cooling performance since its rate of heat removal from the PV back sheet was found to be the highest.