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Inverse problems of recovering heat transfer coefficient from integralmeasurements are considered. The heat transfer coefficient occurs in thetransmission conditions of imperfect contact type or the Robin type boundaryconditions.  It is representable as a finite part of the Fourier series with timedependent coefficients. The additional measurements are integrals of a solutionmultiplied by some weights.  Existence and uniqueness of solutions in Sobolev classes are proven and theconditions on the data are sharp. These conditions include smoothness andconsistency conditions on the data and additional conditions on the kernels ofthe integral operators used in additional measurements. The proof relies on apriori bounds and the contraction mapping principle. The existence anduniqueness theorems are local in time.

Identification of the Heat Transfer Coefficient Using an Inverse Heat Conduction Model