Natural processes driven by heat flow can be understood using quantitative reconstruction of the thermal history of accessory and common minerals that were formed or modified in these processes. Thermochronology assumes that isotopes are lost from minerals by thermally-activated volume diffusion, and forms the basis of many studies of the thermal evolution of the crust. However, some studies challenge this assumption and suggest that the mechanisms controlling isotope transport in minerals over geological time-scales are dominated by aqueous fluid flow within mineral pathways. Here, we test these contrasting hypotheses by inverse modelling apatite uranium–lead (U–Pb) dates to produce theoretical t–T solutions assuming Pb was lost by volume diffusion. These solutions are compared with independent geological constraints and intra-grain apatite U–Pb dates, which demonstrate that volume diffusion governed the displacement of Pb. This confirmation, combined with an inverse-modeling procedure that permits reheating and cooling paths to be distinguished between ∼375 and 570 °C, provides geologists with a unique tool for investigating the high-temperature thermal evolution of accessory minerals using the U–Pb method.