Measurements of the intergalactic medium (IGM) temperature provide a potentially powerful constraint on the reionization history due to the thermal imprint left by the photoionization of neutral hydrogen. However, until recently IGM temperature measurements were limited to redshifts 2 ≤z≤ 4.8, restricting the ability of these data to probe the reionization history at z > 6. In this work, we use recent measurements of the IGM temperature in the near-zones of seven quasars at z∼ 5.8–6.4, combined with a semi-numerical model for inhomogeneous reionization, to establish new constraints on the redshift at which hydrogen reionization completed. We calibrate the model to reproduce observational constraints on the electron scattering optical depth and the H i photoionization rate, and compute the resulting spatially inhomogeneous temperature distribution at z∼ 6 for a variety of reionization scenarios. Under standard assumptions for the ionizing spectra of Population II sources, the near-zone temperature measurements constrain the redshift by which hydrogen reionization was complete to be zr > 7.9 (6.5) at 68 (95) per cent confidence. We conclude that future temperature measurements around other high-redshift quasars will significantly increase the power of this technique, enabling these results to be tightened and generalized.