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The post-reionization thermal state of the intergalactic medium is characterized by a power-law relationship between temperature and density, with a slope determined by the parameter \(\gamma\). We describe a new method to measure \(\gamma\) using the ratio of flux curvature in the Lyman-\(\alpha\) and \(\beta\) forests. At a given redshift, this curvature ratio incorporates information from the different gas densities traced by Lyman-\(\alpha\) and \(\beta\) absorption. It is relatively simple and fast to compute and appears robust against several observational uncertainties. We apply this technique to a sample of 27 high-resolution quasar spectra from the Very Large Telescope. While promising statistical errors on \(\gamma\) appear to be achievable with these spectra, to reach its full potential, the dependence of the curvature ratio on the thermal state of the gas in the foreground Lyman-\(\alpha\) forest will require further, detailed forward modelling.