This paper discusses some problems of the island divertor in the Wendelstein \mbox{7-X} configuration. These islands exist on the ι = 1 surface at the plasma boundary and will be utilized for impurity control in the Wendelstein \mbox{7-X} experiment. The structure of this island region depends on the plasma pressure and the tendency is to become more and more ergodic with rising plasma pressure. Thermal transport in the divertor region is described by the transport equation, which is inherently three-dimensional. By averaging along the helical geometry of the island, this equation can be reduced to a two-dimensional one describing the temperature distribution in the poloidal plane. In this approximation a strong similarity to tokamak geometry exists. Since the plasma currents modify the islands, a finite-β equilibrium is computed as the basis of a geometric analysis of divertor action. Anomalous transport strongly affects the width of the scrape-off layer and the width of the wetted area on the divertor target plates; therefore it is investigated how anomalous transport modifies the transport equation. The non-linearity of the radiation losses in the divertor region and the non-linearity of the boundary conditions can lead to a bifurcation of the temperature distribution and to multiple solutions. Some numerical examples of one-dimensional temperature profiles and bifurcated solutions are given.