The inversion of formerly extensional basins by compressional reactivation of existing faults is believed to be an important mechanism for the exhumation of sedimentary basins. We propose an additional mechanism for the exhumation of some sedimentary basins which does not require compression, and which completely inverts a basin into a dome. In basins formed by intra-crustal density loads, sublithospheric heating, however caused, will reduce the effective elastic thickness of the crust, thereby reactivating subsidence. If the crust is sufficiently weakened that it no longer supports the dense load, we predict the long-term result to be detachment of the load followed by uplift and exhumation of the basin. Finite-element modeling indicates that this can occur for geologically possible load densities in high heat flow regions. Total upward displacement of material from depth can be as much as 10 km in some cases, enough to exhume the basin completely.