The Atacama Large Millimeter/submillimeter Array (ALMA) was used to obtain measurements of spatially and spectrally resolved CH3OH emission from comet C/2012 K1 (PanSTARRS) on 28-29 June 2014. Detection of 12-14 emission lines of CH3OH on each day permitted the derivation of spatially-resolved rotational temperature profiles (averaged along the line of sight), for the innermost 5000 km of the coma. On each day, the CH3OH distribution was centrally peaked and approximately consistent with spherically symmetric, uniform outflow. The azimuthally-averaged CH3OH rotational temperature (T
rot) as a function of sky-projected nucleocentric distance (ρ), fell by about 40 K between ρ= 0 and 2500 km on 28 June, whereas on 29 June, T
rot fell by about 50 K between ρ =0 km and 1500 km. A remarkable (~50 K) rise in T
rot at ρ = 1500-2500 km on 29 June was not present on 28 June. The observed variations in CH3OH rotational temperature are interpreted primarily as a result of variations in the coma kinetic temperature due to adiabatic cooling, and heating through Solar irradiation, but collisional and radiative non-LTE excitation processes also play a role.