  We study a quantity $\mathcal{T}$ defined as the energy U, stored in
non-equilibrium steady states (NESS) over its value in equilibrium $U_0$,
$\Delta U=U-U_0$ divided by the heat flow $J_{U}$ going out of the system. A
recent study suggests that $\mathcal{T}$ is minimized in steady states
(Phys.Rev.E.99, 042118 (2019)). We evaluate this hypothesis using an ideal gas
system with three methods of energy delivery: from a uniformly distributed
energy source, from an external heat flow through the surface, and from an
external matter flow. By introducing internal constraints into the system, we
determine $\mathcal{T}$ with and without constraints and find that
$\mathcal{T}$ is the smallest for unconstrained NESS. We find that the form of
the internal energy in the studied NESS follows $U=U_0*f(J_U)$. In this
context, we discuss natural variables for NESS, define the embedded energy (an
analog of Helmholtz free energy for NESS), and provide its interpretation.
