  We prove a mean field limit, a law of large numbers and a central limit
theorem for a system of point vortices on the 2D torus at equilibrium with
positive temperature. The point vortices are formal solutions of a class of
equations generalising the Euler equations, and are also known in the
literature as generalised inviscid SQG. The mean field limit is a steady
solution of the equations, the CLT limit is a stationary distribution of the
equations.
