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The in-plane thermal conductivity of porous sintered bronze plates was studied both experimentally and numerically. We developed and validated an experimental setup, where the sample was placed in vacuum and heated while its time-dependent temperature field was measured with an infrared camera. The porosity and detailed three-dimensional structure of the samples were determined by X-ray microtomography. Lattice-Boltzmann simulations of thermal conductivity in the tomographic reconstructions of the samples were used to correct the contact area between bronze particles as determined by image analysis from the tomographic reconstructions. Small openings in the apparent contacts could not be detected with the imaging resolution used, and they caused an apparent thermal contact resistance between particles. With this correction included, the behavior of the measured thermal conductivity was successfully explained by an analytical expression, originally derived for regular structures, which involves three structural parameters of the porous structures. There was no simple relationship between heat conductivity and porosity.