The electronic contribution kappa(c) to the thermal conductivity of a two-dimensional superconductor presenting saddle points at the Fermi level in the band structure, corresponding to logarithmic Van Hove singularities in the 2D density of states, is calculated within a variational method. We compare theoretical results obtained for both isotropic s-wave and anisotropic d(x2-y2)-wave gap parameters. The peak structure obverved below T-c on the thermal conductivity of a single crystal of Bi2Sr2CaCu2O8 can be reproduced by considering both gap parameter symmetries whereas the very low temperature behavior of kappa can be only explained by considering a d-wave gap parameter. In this latter case, the Van Hove singularities are found to limit the type of power law dependence of kappa at low temperatures. The model also predicts weak coupling values for the in-plane electron-phonon transport coupling constant lambda(tr) in this material, in agreement with values obtained from the analysis of electrical resistivity data.