In situ measurements of ionospheric and thermospheric temperatures are experimentally challenging because orbiting spacecraft typically travel supersonically with respect to the cold gas and plasma. We present O2+ temperatures in Mars’ ionosphere derived from data measured by the SupraThermal And Thermal Ion Composition (STATIC) instrument onboard the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft. We focus on data obtained during nine special orbit maneuvers known as Deep Dips, during which MAVEN lowered its periapsis altitude from the nominal 150 km to 120 km for one week in order to sample the ionospheric main peak and approach the homopause. We use two independent techniques to calculate ion temperatures from the measured energy and angular widths of the supersonic ram ion beam. After correcting for background and instrument response, we are able to measure ion temperatures as low as 100 K with associated uncertainties as low as 10%. It is theoretically expected that ion and electron temperatures will converge to the neutral temperature at altitudes below the exobase region (~180-200 km) due to strong collisional coupling; however, no evidence of the expected thermalization is observed. We have eliminated several possible explanations for the observed temperature difference between ions and neutrals, including Coulomb collisions with electrons, Joule heating, and heating caused by interactions with the spacecraft. Our current study leaves one plausible heating mechanism, the release of internal energy from O2+ that becomes vibrationally excited as a result of atmospheric chemistry, but future work is needed to assess its validity.