  We present measurements of the thermal Sunyaev-Zel'dovich effect (SZE) toward
SPT-CL J2334-4243 (the Phoenix galaxy cluster) at z=0.597 by the Atacama Large
Millimeter/submillimeter Array (ALMA) in Band 3. The SZE is imaged at 5"
resolution (corresponding to the physical scale of 23kpc/h) within 200kpc/h
from the central galaxy with the peak signal-to-noise ratio exceeding 11.
Combined with the Chandra X-ray image, the ALMA SZE data further allow for
non-parametric deprojection of electron temperature, density, and entropy. Our
method can minimize contamination by the central AGN and the X-ray absorbing
gas within the cluster, both of which largely affect the X-ray spectrum. We
find no significant asymmetry or disturbance in the SZE image within the
current measurement errors. The detected SZE signal agrees well with the
average pressure profile of local cool-core clusters. Unlike any other known
clusters, however, gas temperature drops by at least a factor of 5 toward the
center. We identify ~6x10^{11} M_sun cool gas with temperature ~3keV in the
inner 20kpc/h. Taken together, our results imply that the gas is indeed cooling
efficiently and nearly isobarically down to this radius in the Phoenix cluster.
