The Orion Kleinmann-Low nebula (Orion KL) is the closest region of high-mass star formation to Earth and exhibits a range of physical and chemical components. This makes it an ideal interstellar laboratory for directly observing the interplay between environment and chemistry. We conducted observations of 13CH3OH toward Orion KL with the Atacama Large Millimeter/submillimeter Array (ALMA), from which we mapped physical parameters toward the nebula at angular resolutions of ~0.2" and 0.7" to look at variation of these parameters on spatial scales smaller than previous observations. Using pixel-by-pixel spectral line fitting, we mapped the velocity field, line widths, rotational temperature, and 13CH3OH column density across Orion KL on local spatial scales. The mechanism by which methanol is injected into the gas phase remains uncertain despite theoretical and experimental work pointing to its formation on the surfaces of icy grains. From our high spatial resolution maps, we conclude that the observed 13CH3OH is predominantly the result of thermal desorption in Orion KL. Not only does this provide some additional constraints on interstellar methanol chemistry, but it also demonstrates the utility of high spatial resolution mapping of interstellar molecules.