Plasmonic catalysts use light to drive chemical reactions. One critical question is how light energy moves at nanoscales in these complex systems, leading to chemical transformations. In this contribution, we map out this energy flow by developing approaches to measure spatial temperature distributions in heterogeneous plasmonic catalysts, consisting of three-dimensional networks of plasmonic nanoparticles anchored on an oxide support. We survey the local temperatures of molecules adsorbed on catalytically active plasmonic nanoparticles, the nanoparticles themselves, and the catalyst support, under steady-state continuous-wave illumination. We reveal the existence of large temperature gradients, in which the local temperatures of the molecules, nanoparticles, and the surrounding environment can vary greatly. We show that these temperature gradients are a natural consequence of plasmon relaxation, involving the interconversion between electromagnetic light energy, electronic excitations, and heating of various entities as these electronic excitations relax. The presence of these gradients is a fundamental and unique feature of gas-phase plasmonic catalysis.