We present measurements of spatially and spectrally resolved CH3OH emission from the coma of comet C/2012 K1 (PanSTARRS) observed using the Atacama Large Millimeter/submillimeter Array (ALMA) in June 2014. The CH3OH distribution is centrally peaked, with a spatial profile consistent with production from the sublimation of ices from the nucleus. From the detection of seven strong CH3OH lines in the J = 7 - 6 band, the line-of-sight average rotational excitation temperature (Trot) is derived as a function of distance across the coma. At the CH3OH peak, we find T-rot = 92 +/- 6 K, falling to about 40 K at a distance of 1000 km.