  Inverse problems of recovering heat transfer coefficient from integral
measurements are considered. The heat transfer coefficient occurs in the
transmission conditions of imperfect contact type or the Robin type boundary
conditions.
  It is representable as a finite part of the Fourier series with time
dependent coefficients. The additional measurements are integrals of a solution
multiplied by some weights.
  Existence and uniqueness of solutions in Sobolev classes are proven and the
conditions on the data are sharp. These conditions include smoothness and
consistency conditions on the data and additional conditions on the kernels of
the integral operators used in additional measurements. The proof relies on a
priori bounds and the contraction mapping principle. The existence and
uniqueness theorems are local in time.
