The Potts model is a discrete Markov random field that can be used to label the pixels in an image according to an unobserved classification. The strength of spatial dependence between neighbouring labels is governed by the inverse temperature parameter. This parameter is difficult to estimate, due to its dependence on an intractable normalising constant. Several approaches have been proposed, including the exchange algorithm and approximate Bayesian computation (ABC), but these algorithms do not scale well for images with a million or more pixels. We introduce a precomputed binding function, which improves the elapsed runtime of these algorithms by two orders of magnitude. Our method enables fast, approximate Bayesian inference for computed tomography (CT) scans and satellite imagery. This is joint work with Kerrie Mengersen, Tony Pettitt and Chris Drovandi at QUT, and Christian Robert at the University of Warwick and Université Paris Dauphine.