  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.
