The Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI) is a satellite experiment scheduled to launch on NASA's Ionospheric Connection Explorer (ICON) in 2017. MIGHTI is designed to measure horizontal neutral winds and neutral temperatures in the terrestrial thermosphere. Temperatures will be inferred by imaging the molecular oxygen Atmospheric band (A band) on the limb in the lower thermosphere. MIGHTI will measure the spectral shape of the A band using discrete wavelength channels to infer the ambient temperature from the rotational envelope of the band. Here we present simulated temperature retrievals based on the as-built characteristics of the instrument and the expected emission rate profile of the A band for typical daytime and nighttime conditions. We find that for a spherically symmetric atmosphere, the measurement precision is 1 K between 90-105 km during the daytime whereas during the nighttime it increases from 1 K at 90 km to 3 K at 105 km. We also find that the accuracy is 2 K to 11 K for the same altitudes. The expected MIGHTI temperature precision is within the measurement requirements for the ICON mission.