A generalized definition of temperature, which holds both for equilibrium and nonequilibrium states, is proposed. Then, two conceivable relations between the generalized temperature and the internal energy per unit mass are considered, for a medium at constant density. These assumptions split the theory of internal-energy waves, recently presented by the authors, in two theories of generalized-temperature waves, which can be checked experimentally by means of thermometers. The predictions of these theories are compared. © 1998 The American Physical Society.