  We consider the evolution of the temperature $u$ in a material with thermal
memory characterized by a time-dependent convolution kernel $h$. The material
occupies a bounded region $\Omega$ with a feedback device controlling the
external temperature located on the boundary $\Gamma$. Assuming both $u$ and
$h$ unknown, we formulate an inverse control problem for an integrodifferential
equation with a nonlinear and nonlocal boundary condition. Existence and
uniqueness results of a solution to the inverse problem are proved.
