The heights of hotspot volcanoes are modeled by assuming isostatic equilibrium between the magma column and the adjacent lithosphere. The depth to the level of compensation is assumed to be related to the thickness of the lithosphere after it has been reheated and thinned by a hotspot. There is a square-root relationship between volcano heigh and lithospheric age. Relationships between volcano height and lithospheric thickness and between volcano height and lithospheric age. Relationships between volcano height and lithospheric thickness and between reheated thickness and age of the lithosphere can be consrained within the limits imposed by uncertainties in lithospheric and magma densities. If the reheated thickness determined from the isostatic model can be compared with lithospheric thickness determined from thermal models of the lithosphere, then a relationship between the thickness of the lithosphere before and after reheating can be derived. Combining the upper limit on the reheated thickness/age relationship with a theoretical expression, derived by S. T. Crough, which relates swell height to lithospheric age, reset thickness, and physical consants, yields a swell-height/age relationship that is in good agreement with empirical swell-height data. This agreement supports the assumption that the lithospheric thickness defined isostatically by volcano heights is closely related to the thermal thickness of the lithosphere, a result that, in turn, supports the thermal origin of hotspot swells.