We derive a self-similar description for the 2D streamline topology and flow structure of an axi-symmetric, thermally driven wind originating from a disc in which the density is a power law function of radius. Our scale-free solution is strictly only valid in the absence of gravity or centrifugal support; comparison with 2D hydrodynamic simulations of winds from Keplerian discs however demonstrates that the scale-free solution is a good approximation also in the outer regions of such discs, and can provide a reasonable description even for launch radii well within the gravitational radius of the flow. Although other authors have considered the flow properties along streamlines whose geometry has been specified in advance, this is the first isothermal calculation in which the flow geometry and variation of flow variables along streamlines is determined self-consistently. It is found that the flow trajectory is very sensitive to the power-law index of radial density variation in the disc: the steeper the density gradient, the stronger is the curvature of streamlines close to the flow base that is required in order to maintain momentum balance perpendicular to the flow. Steeper disc density profiles are also associated with more rapid acceleration, and a faster fall-off of density, with height above the disc plane. The derivation of a set of simple governing equations for the flow structure of thermal winds from the outer regions of power law discs offers the possibility of deriving flow observables without having to resort to hydrodynamical simulation.