Textbook in PDF format This book puts together non-equilibrium thermodynamics, heat transport properties of superfluid He II, and thermodynamic and dynamic aspects of quantum turbulence. A one-fluid extended model of superfluid helium, with heat flux as an additional independent variable, is presented and compared with the two-fluid model, to explore how both models complement each other. Important features arise in rotating situations and in superfluid turbulence, characterized by quantized vortices leading to strong nonlinearities between heat flux and temperature gradient. The dynamics of vortex lines and their interaction with heat dynamics, a central topic in superfluid turbulence, is dealt with by introducing the vortex line density as an independent variable and writing its dynamical equations, considering the transitions from laminar to turbulent flows and from diffusive to ballistic regimes. Classical and quantum turbulence are compared from a mesoscopic view and from their energy spectra