The one-dimensional nonlinear inverse heat conduction problem is considered. A new technique for estimating the surface variances of the predicted surface fluxes and temperatures based on an adjoint formulation is presented. The surface variances are related to the measurement variances and to an estimate of the initial condition variances. The only assumption necessary to apply the technique is that of additive measurement errors. Two test cases with three sets of boundary conditions are studied. The surface variance estimates given by the adjoint formulation and direct estimation are shown to be in good agreement.