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A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked out to 10th order for the surface coupled to a q-state Potts model. Accurate estimates for, e.g., γ_str are obtained both in the low q (c<1) and high q (branched polymer) regimes, including the logarithmic corrections to scaling.arXiv:hep-th/9505087v1 fatcat:isglaeykdfgalppryjuidqm544