  We study spatial correlations in the transport of energy between two baths at
different temperatures. To do this, we introduce a minimal model in which
energy flows from one bath to another through two subsystems. We show that the
transport-induced energy correlations between the two subsystems are of the
same order as the energy fluctuations within each subsystem. The correlations
can be either positive or negative and we give bounds on their values which are
associated with a dynamic energy scale. The different signs originate as a
competition between fluctuations generated near the baths, and fluctuations of
the current between the two subsystems. This interpretation sheds light on
known results for spatially-dependent heat and particle conduction models.
