  We develop and apply a minimally invasive approach for characterization of
inter-species spin interactions by detecting spin fluctuations alone. We
consider a heterogeneous two-component spin ensemble in thermal equilibrium
that interacts via binary exchange coupling, and we determine
cross-correlations between the intrinsic spin fluctuations exhibited by the two
species. Our theoretical predictions are experimentally confirmed using
`two-color' optical spin noise spectroscopy on a mixture of interacting Rb and
Cs alkali vapors. The results allow us to explore the rates of spin exchange
and total spin relaxation under conditions of strict thermodynamic equilibrium.
