  We consider a quantum system of fixed size consisting of a regular chain of
$n$-level subsystems, where $n$ is finite. Forming groups of $N$ subsystems
each, we show that the strength of interaction between the groups scales with
$N^{- 1/2}$. As a consequence, if the total system is in a thermal state with
inverse temperature $\beta$, a sufficient condition for subgroups of size $N$
to be approximately in a thermal state with the same temperature is $\sqrt{N}
\gg \beta \bar{\delta E}$, where $\bar{\delta E}$ is the width of the occupied
level spectrum of the total system. These scaling properties indicate on what
scale local temperatures may be meaningfully defined as intensive variables.
This question is particularly relevant for non-equilibrium scenarios such as
heat conduction etc.
