We present measurements of the thermal Sunyaev-Zeldovich 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.
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