A mathematical model predicting the heat transport capability in a miniature flat heat pipe (FHP) with a wired wick structure was developed to analytically determine its maximum heat transport rate including the capillary limit. The effects of gravity on the profile of the thin-film-evaporation region and the distribution of the heat flux along a curved surface were investigated. The heat transfer characteristics of the thin-film evaporation on the curved surface were also analyzed and compared with that on a flat surface. Combining the analysis on the thin-film-condensation heat transfer in the condenser, the model can be used to predict the total temperature drop between the evaporator and condenser in the FHP. In order to verify the model, an experimental investigation was conducted. The theoretical results predicted by the model agree well with the experimental data for the heat transfer process occurring in the FHP with the wired wick structure. Results of the investigation will assist in the optimum design of the curved-surface wicks to enlarge the thin-film-evaporation region and a better understanding of heat transfer mechanisms in heat pipes.