What is the meaning of the thermodynamical temperature in quantum mechanics? What is its role in the classical limit? What can we say about the interplay between quantum and thermal fluctuations? Can we impose a constant-temperature constraint within dynamical simulations of quantum systems as we do in simulations of classical systems? These questions will be reviewed here. In particular, it will be shown how a quantum version of the celebrated Nos'e constant-temperature dynamics can be defined within the phase space formulation of quantum mechanics.