Exciton polaritons constitute a unique realization of a quantum fluid interacting with its environment. Using selenide-based microcavities, we exploit this feature to warm up a polariton condensate in a controlled way and monitor its spatial coherence. We determine directly the amount of heat picked up by the condensate by measuring the phonon-polariton scattering rate and comparing it with the loss rate. We find that, upon increasing the heating rate, the spatial coherence length decreases markedly, while localized phase structures vanish, in good agreement with a stochastic mean-field theory. From the thermodynamical point of view, this regime is unique, as it involves a nonequilibrium quantum fluid with no well-defined temperature but which is nevertheless able to pick up heat with dramatic effects on the order parameter.