The relationship between the Near-Earth Objects (3200) Phaethon and (155140) 2005 UD is unclear. While both are parents to Meteor Showers, (the Geminids and Daytime Sextantids, respectively), have similar visible-wavelength reflectance spectra and orbits, dynamical investigations have failed to find any likely method to link the two objects in the recent past. Here we present the first near-infrared reflectance spectrum of 2005 UD, which shows it to be consistently linear and red-sloped unlike Phaethons very blue and concave spectrum. Searching for a process that could alter some common starting material to both of these end states, we hypothesized that the two objects had been heated to different extents, motivated by their near-Sun orbits, the composition of Geminid meteoroids, and previous models of Phaethons surface. We thus set about building a new laboratory apparatus to acquire reflectance spectra of meteoritic samples after heating to higher temperatures than available in the literature to test this hypothesis and were loaned a sample of the CI Chondrite Orgueil from the Vatican Meteorite Collection for testing. We find that while Phaethons spectrum shares many similarities with different CI Chondrites, 2005 UDs does not. We thus conclude that the most likely relationship between the two objects is that their similar properties are only by coincidence as opposed to a parent-fragment scenario, though the ultimate test will be when JAXAs DESTINY+ mission visits one or both objects later this decade. We also discuss possible paths forward to understanding Phaethons properties from dynamical and compositional grounds.