Explosive volcanic eruptions are driven by exsolution of H2O-rich vapour from silicic magma. Eruption dynamics involve a complex interplay between nucleation and growth of vapour bubbles and crystallization, generating highly nonlinear variation in the physical properties of magma as it ascends beneath a volcano. This makes explosive volcanism difficult to model and, ultimately, to predict. A key unknown is the temperature variation in magma rising through the sub-volcanic system, as it loses gas and crystallizes en route. Thermodynamic modelling of magma that degasses, but does not crystallize, indicates that both cooling and heating are possible. Hitherto it has not been possible to evaluate such alternatives because of the difficulty of tracking temperature variations in moving magma several kilometres below the surface. Here we extend recent work on glassy melt inclusions trapped in plagioclase crystals to develop a method for tracking pressure-temperature-crystallinity paths in magma beneath two active andesite volcanoes. We use dissolved H2O in melt inclusions to constrain the pressure of H2O at the time an inclusion became sealed, incompatible trace element concentrations to calculate the corresponding magma crystallinity and plagioclase-melt geothermometry to determine the temperature. These data are allied to ilmenite-magnetite geothermometry to show that the temperature of ascending magma increases by up to 100 degrees C, owing to the release of latent heat of crystallization. This heating can account for several common textural features of andesitic magmas, which might otherwise be erroneously attributed to pre-eruptive magma mixing.