ALMA observations in continuum emission reveal rich annular structure in protoplanetary disks. Attributing the existence of such features to embedded planets is a popular scenario, supported by studies using hydrodynamics models. Recent work has shown that radiative cooling greatly influences the capability of planet-driven spirals to transport angular momentum, ultimately deciding the number, position, and depth of rings and gaps that a planet can shape into the disk. However, radiation transport has only been treated as a local cooling law, not taking into account the extended structure of spiral arms. We compare the previous state-of-the-art models of planet?disk interaction with radiation hydrodynamics to models with full treatment of vertical and in-plane cooling, and show that different cooling mechanisms dominate in different regimes. We follow up with synthetic emission maps of ALMA systems, and show that our models reproduce best the observations found in the literature. We conclude that appropriate treatment of radiation transport is key to constraining the parameter space in reproducing ALMA observations with the planet?disk interaction scenario.