Partition function for a system in local thermal equilibrium

For a system in equilibrium, the partition function is standard.
But if the system is in local thermal equilibrium but stationary (i.e. zero or negligible time variation), but the temperature varies spatially, how can one calculate the partition function?

To clarify the question, let us take a sample system. Let there be some thermal medium in a uniform cylindrical tube of finite length $L$. Let one end of the tube be maintained at temperature $T1$, and the other end at $T2$, where $T1 neq T2$. $T1$ and $T2$ are constant in time (no time variation). What would be the partition function for this system?