We consider an axisymmetric inverse problem for the heat equation inside the cylinder a ≤ r ≤ b. We wish to determine the surface temperature on the interior surface {r = a} from the Cauchy data on the exterior surface {r = b}. This problem is ill-posed. Using the Laplace transform, we solve the direct problem. Then the inverse problem is reduced to a Volterra integral equation of the first kind. A standard Tikhonov regularization method is applied to the approximation of this integral equation when the data is not exact. Some numerical examples are given to illustrate the stability of the proposed method. MSC: 35K05; 65N06; 35R30; 44A10

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