The oxygen isotopic composition of vertebrate bone phosphate (delta(p)) is related to ingested water and to the body temperature at which the bone forms. The delta(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 deltap variation. Values of delta(p) from a well-preserved Tyrannosaurus rex suggest that this species maintained homeothermy with less than 4 degrees C of variability in body temperature. Maintenance of homeothermy implies a relatively high metabolic rate that is similar to that of endotherms.