Two-dimensional conductive thermal models of an evolving metamorphic core complex provide insights into synextensional and postextensional thermal history. The models assume a rotating-hinge geometry with a low-angle (20¿--30¿) detachment fault that flattens out at a depth of 12--15 km. Simulations reveal details of the temperature-time paths experienced by footwall rocks during extension that have significant implications for interpretation of thermochronological data. The evolving isotherms are roughly horizontal near the surface breakout of the detachment fault and at depth are rotated toward the detachment ramp angle as the ramp-flat interface is approached. This leads to highly curved apparent geothermal gradients along the detachment fault surface, with local gradients near the surface being up to 3 times those at depth. Cooling accelerates as rocks approach the surface, and rates vary by up to an order of magnitude with position within the unroofing footwall block and the temperature interval in question. Isotherms advance upward along the detachment fault surface as extension progresses. As a result, calculations of extension rate made by plotting 40Ar/39Ar or fission-track dates against distance along the detachment slip direction can underestimate the true rate by up to 40%. Estimates of detachment dip can be similarly affected by the nonlinearity of the along-fault synextensional thermal gradient. Simulation of cooling paths in the D'Entrecasteaux Islands core complex in Papua New Guinea reveals a remarkable congruence between model predictions and the cooling path determined from P-T-t data. The models also serve to examine possible mechanisms behind the heat flow low of 20--40% that parallels the band of core complexes in Arizona and southern California. The present-day heat-flow patterns and low-relief Moho are most closely matched by a balanced geometry in which unroofing of the core complex is compensated by pure shear extension off center from the complex, with the core itself being a megaboudin of little or no internal shear. This geometry may also be analogous to a scenario in which lower crustal flow compensates for tectonic denudation. However, models based on detailed heat-production data from the Santa Catalina Mountains suggest that core-complex formation may not be responsible for the low heat flow in that area. Furthermore, the net amount of extension in area-balanced crustal cross sections based on Arizona core complexes does not appear to be sufficient to explain the high heat flow that characterizes the overall southern Basin and Range, indicating that additional sources of heat over that introduced by regional extension may be required to explain the regional thermal anomaly. ¿ American Geophysical Union 1996