Model composite plates composed of highly conductive slender copper fibres impregnated with a poorly conductive and transparent PMMA matrix were processed with different fibrous architectures, i.e. with various controlled fibre contents and orientations. Their microstructure was characterised using both optical observations and X-ray microtomography. Their in-plane thermal conductivity was measured by using a specific testing apparatus combined with an inverse modelling method. Results point out the strong link between the anisotropy of the in-plane conductivity and of the microstructure. The role of the fibre content on the conductivity is also emphasised. An analytical conduction model which accounts for the influence of the fibre content, the orientation, the aspect ratio and the thermal resistances at fibre-fibre contacts, was proposed and its predictions were compared with the experimental results. Using only one fitting parameter, namely the conductance at fibre-fibre contacts, this model shows a good prediction of all the experiments.