Changes of sample temperature associated with small adiabatic pressure changes were measured for the metals aluminum, copper, indium, iron, and lead, and the thermodynamic Gr¿neisen parameter &ggr; is calculated from the relation &ggr;= (Ks/T) (∂T/∂P)s where Ks is the adiabatic bulk modulus. Measurements were carried out to 33 kbar under hydrostatic conditions in a fluid cell with Bridgman's unsupported seals using an end-loaded piston cylinder apparatus.