  We investigate the dynamics of thermal Casimir interactions between plates
described within a living conductor model, with embedded mobile anions and
cations, whose density field obeys a stochastic partial differential equation
which can be derived starting from the Langevin equations of the individual
particles. This model describes the thermal Casimir interaction in the same way
that the fluctuating dipole model describes van der Waals interactions. The
model is analytically solved in a Debye-H\"uckel-like approximation. We
identify several limiting dynamical regimes where the time dependence of the
thermal Casimir interactions can be obtained explicitly. Most notably we find a
regime with diffusive scaling, even though the charges are confined to the
plates and do not diffuse into the intervening space, which makes the diffusive
scaling difficult to anticipate and quite unexpected on physical grounds.
