  We extend a previously developed approach to relate thermal currents in the
high temperature regime and classical limits of amplitudes. We consider the
bi-adjoint scalar theory, which has the basic structure of a cubic theory and
which is related to QCD and gravity through the double copy. In addition, we
consider a generalization of scalar QED to model classical spin, where massive
scalars are complex higher-spin fields. We derive Vlasov-type kinetic equations
for bi-adjoint scalars and study their iterative solutions, while for QED we
use well-known kinetic equations. In both cases we find consistency between
these solutions and the amplitude-like approach.
