A phase of isobaric heating during exhumation of high-pressure rocks is often reported, but the tectonic significance of isobaric heating remains uncertain. Constraining the timescales of isobaric heating is essential for connecting the heating to tectonic processes of lithospheric thickening and extension. An isobaric heating phase has been reported for the Cycladic Blueschist Unit in the Hellenide orogen of Greece. We present diffusion modeling of major elements in garnet using data from Naxos Island to provide new independent estimates of the duration of isobaric heating. We also present radioactive trace element analyses of the Cycladic basement and a heat conduction model to explore the heat production generated in the basement and its influence on isobaric heating. Our model indicates that isobaric heating occurred over ∼9.7 Myr, during which the Cycladic basement generated enough heat to explain the observed temperature increase. At the end of this heating phase, the temperature increase caused a significant drop in crustal strength, which controlled the style of crustal extensional deformation during subsequent rollback of the subducting slab. Our work implies that the underthrusting of radiogenic material in convergent settings produces sufficient heat to significantly increase temperature which weakens the crust and enables pervasive deformation.