The oxygen isotopic composition of vertebrate bone phosphate (δ_p) is related to ingested water and to the body temperature at which the bone forms. The δ_p is in equilibrium with the individual's body water, which is at a physiological steady state throughout the body. Therefore, intrabone temperature variation and the mean interbone temperature differences of well-preserved fossil vertebrates can be determined from the δ_p variation. Values of δ_p from a well-preserved Tyrannosaurus rex suggest that this species maintained homeothermy with less than 4^circC of variability in body temperature. Maintenance of homeothermy implies a relatively high metabolic rate that is similar to that of endotherms.