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If two phases of a certain material exist at the same time, e.g., a gas and aliquid, they have the same temperature. This fundamental law of equilibriumphysics is known to apply even to many non-equilibrium systems. However,recently, there has been much attention in the finding that inertialself-propelled particles like Janus colloids in a plasma, microflyers, orbeetles at interfaces could self-organize into a hot gas-like phase thatcoexists with a colder liquid-like phase. Here, we show that a kinetictemperature difference across coexisting phases can occur even in equilibriumsystems when adding generic (overdamped) self-propelled particles. In thiscase, surprisingly, we find that the dense phase (liquid) cannot only be colderbut also hotter than the dilute phase (gas). This generic effect hinges oncorrelated events where active particles collectively push and heat up passiveones, which can overcompensate their collision-induced energy loss locally. Ourresults answer the fundamental question if a non-equilibrium gas can be colderthan a coexisting liquid and create a route to equip matter with self-organizeddomains of different kinetic temperatures.

Motility-induced coexistence of a hot liquid and a cold gas