The Mu2e experiment at Fermilab uses three superconducting solenoid magnets cooled to nominally 4.5 K with 80-K thermal shields and heat intercepts; they are in the order: production solenoid (PS), transfer solenoid (TS), and detector solenoid (DS). The cryogenic system is comprised of a refrigerator unit, a distribution box, feed boxes, and transfer lines to the solenoids. A thermosiphon cooling scheme is envisioned for the PS and DS, whereas the TS will use forced flow cooling. This paper focuses on the feedbox for the PS. Helium at 4.8 K and 3 bar is supplied from the distribution box to a subcooler helium vessel contained in the feedbox. Helium (He) is introduced in the magnet thermosiphon cooling circuit and is also used to conductively cool and intercept heat along the transfer lines. A nominally 80-K thermal shield is employed and actively cooled by liquid nitrogen (LN2), which is also used to intercept heat at 80 K in the high-temperature superconductor power leads. A preliminary 3-D CAD model of the feedbox will be introduced, and thermal calculations and optimization of the main elements aimed to reduce the heat loads to the 80-and 4.6-K levels will be thoroughly discussed.