We observed two eclipses of the Kepler-13A planetary system, on UT 2014 April 28 and UT 2014 October 13, in the near-infrared using Wide Field Camera 3 on the Hubble Space Telescope. By using the nearby binary stars Kepler-13BC as a reference, we were able to create a differential light curve for Kepler-13A that had little of the systematics typically present in HST/WFC3 spectrophotometry. We measure a broadband (1.1–1.65 μm) eclipse depth of 734 ± 28 ppm and are able to measure the emission spectrum of the planet at R ≈ 50 with an average precision of 70 ppm. We find that Kepler-13Ab possesses a noninverted, monotonically decreasing vertical temperature profile. We exclude an isothermal profile and an inverted profile at more than 3σ. We also find that the dayside emission of Kepler-13Ab appears generally similar to an isolated M7 brown dwarf at a similar effective temperature. Due to the relatively high mass and surface gravity of Kepler-13Ab, we suggest that the apparent lack of an inversion is due to cold-trap processes in the planet’s atmosphere. Using a toy model for where cold traps should inhibit inversions, as well as observations of other planets in this temperature range with measured emission spectra, we argue that with more detailed modeling and more observations we may be able to place useful constraints on the size of condensates on the daysides of hot Jupiters.