  In this work we present a computation of the averages of conserved charge
densities and currents of (1+1)-dimensional Integrable Quantum Field Theories
in Generalised Gibbs Ensembles. Our approach is based on the quasi-particle
description provided by the Thermodynamic Bethe Ansatz combined with the
principles of Generalised Hydrodynamics, and we focus on Non-Equilibrium Steady
State averages. When considering the ultraviolet (i.e. high temperature) limit
of such averages, we recover the famous result by Bernard and Doyon (2012) for
the energy current and density in Conformal Field Theories, and we extend it to
conserved quantities with spin $s > 1$. We show that their averages are
proportional to $T_L^{s+1}\pm T_R^{s+1}$, with $T_L$, $T_R$ the temperatures of
two asymptotic thermal reservoirs. The same power law is obtained when
considering some non-thermal generalised Gibbs states. In Conformal Field
Theory, the power law is a consequence of the transformation properties of
conserved charge operators, while the proportionality coefficient depends on
the spin of the operator and on the central charge of the theory. We present an
exact analytic expression for this coefficient in the case of a massive free
fermion. At equilibrium, proportionality of spin-$s$ density averages to
$T^{s+1}$ can be thought of as a generalisation of Stefan-Boltzmann's law,
which states that the energy per unit surface area radiated by a black body
scales as $T^4$.
