We refine conventional continental-scale geodynamic models by including conversion of mechanical work done by deformation into heat. The intensity of the shear heating is extracted from the Brace-Goetze strength envelope without any additional model parameters or assumptions. Incorporation of this, certainly present, heating rate into a model may result in up to tenfold stress reduction, which is exceeding the effects of variation of common parameters within their uncertainty limits. Shear heating with lithospheric thickening at high integrated strength solves the puzzle of the heretofore-missing heat source recorded by metamorphism, magmatism, and heat flow in mountain building. However, the mechanism is self-limiting as the rising temperature reduces stress and thus the rate of heat production. Thus this is a self-regulating mechanism maintaining a moderate integrated lithospheric strength consistent with results of model-independent force-balanced calculations and with surface heat flow measurements.