Using a steady-state 2-D network model to simulate the thermal behaviour of copper and superalloy matrix composites, reinforced with different types of randomly distributed continuous fibers, the limit values of thermal conductivity are established for the analysed composites. A large number of random distributions for each matrix-fiber combination is tested to assess the accuracy of the numerical results. The influence of the type of fiber, its distribution and its proportion is shown graphically. Examples of continuous fiber metal matrix composites (continuous MMCs), such as those of copper and Incoloy 907 matrices, are studied.