Nosé-Hoover-like simulation schemes are derived in the unifying framework introduced by Grmela [Phys. Lett. A 174 (1993) 59]. The governing equations are shown to represent a Hamiltonian system. The Hamiltonian is the thermodynamic potential and the structure in the state space is the Poisson structure combining the canonical Poisson structure of particle dynamics with the non-canonical Poisson structure of hydrodynamics.