We revisit the new theory for a thermoviscous fluid developed by Green and Naghdi [A.E. Green, P.M. Naghdi, A new thermoviscous theory for fluids, J. Non-Newtonian Fluid Mech. 56 (1995) 289-306]. By adopting a different strategy to the constitutive theory we derive a fully consistent thermodynamic theory for a dissipationless fluid. We believe this is more natural than the approach used for a dissipationless flow in Green and Naghdi [A.E. Green, P.M. Naghdi, A new thermoviscous theory for fluids, J. Non-Newtonian Fluid Mech. 56 (1995) 289-306]. A fully nonlinear acceleration wave analysis is sketched for our theory when the wave is entering a region of equilibrium. (C) 2007 Elsevier B.V. All rights reserved.