The Atacama Large Millimeter/submillimeter Array (ALMA) was used to obtain measurements of spatially and spectrally resolved CH$_3$OH emission from comet C/2012 K1 (PanSTARRS) on 28-29 June 2014. Detection of 12-14 emission lines of CH$_3$OH 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 CH$_3$OH distribution was centrally peaked and approximately consistent with spherically symmetric, uniform outflow. The azimuthally-averaged CH$_3$OH rotational temperature ($T_{rot}$) as a function of sky-projected nucleocentric distance ($rho$), fell by about 40 K between $rho=0$ and 2500 km on 28 June, whereas on 29 June, $T_{rot}$ fell by about 50 K between $rho=$0 km and 1500 km. A remarkable ($sim50$ K) rise in $T_{rot}$ at $rho=$1500-2500 km on 29 June was not present on 28 June. The observed variations in CH$_3$OH 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.
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