  The thermal response of nonequilibrium systems requires the knowledge of
concepts that go beyond entropy production. This is showed for systems obeying
overdamped Langevin dynamics, either in steady states or going through a
relaxation process. Namely, we derive the linear response to perturbations of
the noise intensity, mapping it onto the quadratic response to a constant small
force. The latter, displaying divergent terms, is explicitly regularized with a
novel path-integral method. The nonequilibrium equivalents of heat capacity and
thermal expansion coefficient are two applications of this approach, as we show
with numerical examples.
