  We compute higher order contributions to the free energy of noncommutative
quantum electrodynamics at a nonzero temperature $T$. Our calculation includes
up to three-loop contributions (fourth order in the coupling constant $e$). In
the high temperature limit we sum all the {\it ring diagrams} and obtain a
result which has a peculiar dependence on the coupling constant. For large
values of $e\theta T^2$ ($\theta$ is the magnitude of the noncommutative
parameters) this non-perturbative contribution exhibits a non-analytic behavior
proportional to $e^3$. We show that above a certain critical temperature, there
occurs a thermodynamic instability which may indicate a phase transition.
