Abstract Intrusion and underplating of mafic magmas tend to facilitate continental extension by thermatically weakening the lithosphere. However, adding rheologically hard mafic material to the crust also strengthens the lithosphere. We have investigated the time-dependent competing effects of thermal weakening and rheological hardening using a simple numerical model, and compared the results with the spatial and temporal developments of Tertiary tectonomagmatism in the North American Cordillera. The close temporal-spatial correlation between magmatism and formation of metamorphic core complexes in the Cordillera was consistent with model predictions when a relatively cold lithospheric mantle was assumed. In addition to thermally weakening the lithosphere, magma intrusion may have facilitated core-complex formation by reducing the effective viscosity of the lower crust, allowing crustal collapse to be decoupled from the mantle and to occur at relatively low stress levels. The complicated spatial and temporal patterns of tectonomagmatism in the Great Basin since the mid-Tertiary were predictable with intrusion and underplating of mafic magmas in conjunction with significant lithospheric thinning. Depending on the thermal structure of the lithosphere and the nature of mafic intrusion, the minimum lithospheric strength may lag the peak volcanism by a few million years; and the center of major volcanic fields may become relatively stronger than the surrounding areas because of rheological hardening.