  We consider a coupled linear system describing a thermoviscoelastic plate
with hereditary effects. The system consists of a hyperbolic
integrodifferential equation, governing the temperature, which is linearly
coupled with the partial differential equation ruling the evolution of the
vertical deflection, presenting a convolution term accounting for memory
effects. It is also assumed that the thermal power contains a memory term
characterized by a relaxation kernel. We prove that the system is exponentially
stable and we obtain a closeness estimate between the system with memory
effects and the corresponding memory-free limiting system, as the kernels fade
in a suitable sense.
