  The high volatility of renewable energies calls for more energy efficiency.
Thus, different physical systems need to be coupled efficiently although they
run on various time scales. Here, the port-Hamiltonian (pH) modeling framework
comes into play as it has several advantages, e.g., physical properties are
encoded in the system structure and systems running on different time scales
can be coupled easily. Additionally, pH systems coupled by energy-preserving
conditions are still pH. Furthermore, in the energy transition hydrogen becomes
an important player and unlike in natural gas, its temperature-dependence is of
importance. Thus, we introduce an infinite dimensional pH formulation of the
compressible non-isothermal Euler equations to model flow with
temperature-dependence. We set up the underlying Stokes-Dirac structure and
deduce the boundary port variables. We introduce coupling conditions into our
pH formulation, such that the whole network system is pH itself. This is
achieved by using energy-preserving coupling conditions, i.e., mass
conservation and equality of total enthalpy, at the coupling nodes.
Furthermore, to close the system a third coupling condition is needed. Here,
equality of the outgoing entropy at coupling nodes is used and included into
our systems in a structure-preserving way. Following that, we adapt the
structure-preserving aproximation methods from the isothermal to the
non-isothermal case. Academic numerical examples will support our analytical
findings.
