  We review a recent approach to determine the minimal spatial length scales on
which local temperature exists. After mentioning an experiment where such
considerations are of relevance, we first discuss the precise definition of the
existence of local temperature and its physical relevance. The approach to
calculate the length scales in question considers homogenous chains of
particles with nearest neighbor interactions. The entire chain is assumed to be
in a thermal equilibrium state and it is analyzed when such an equilibrium
state at the same time exists for a local part of it. The result yields
estimates for real materials, the liability of which is discussed in the
sequel. We finally consider a possibility to detect the existence or
non-existence of a local thermal state in experiment.
