This paper aims to present an effective two-dimensional inverse heat conduction technique and an experimental design for accurately estimating the local convective heat transfer coefficient of vapor condensation over a conical surface, given temperature measurements at some interior locations. The functional form for the heat transfer coefficient is not known a priori. The method uses a sequential procedure together with Beck's function specification approach. Solution accuracy and the effects of experimental errors are examined using simulated temperature data. It is concluded that a good estimation of space-variable heat transfer coefficient can be made from the knowledge of transient temperature recordings using the proposed inverse heat conduction problem method. The method is also used in a series of numerical experiments to provide the optimum experimental design for condensation heat transfer investigation.