We have obtained new resolved images of the well-studied HR 4796A dust ring at 18 and 25 microns with the 8-meter Gemini telescopes. These images confirm the previously observed spatial extent seen in mid-IR, near-IR, and optical images of the source. We detect brightness and temperature asymmetries such that dust on the NE side is both brighter and warmer than dust in the SW. We show that models of so-called pericenter glow account for these asymmetries, thus both confirming and extending our previous analyses. In this scenario, the center of the dust ring is offset from the star due to gravitational perturbations of a body with an eccentric orbit that has induced a forced eccentricity on the dust particle orbits. Models with 2-micron silicate dust particles and a forced eccentricity of 0.06 simultaneously fit the observations at both wavelengths. We also show that parameters used to characterize the thermal-emission properties of the disk can also account for the disk asymmetry observed in shorter-wavelength scattered-light images.