It is indicated that the solder joint of the metal fibrous materials is a critical factor impacting the heat conduction. To reveal the mechanism by which solder joint sizes, solder joint skips, solder flux materials, and filling media affect the thermal conductivity of fibres, pore-scale numerical simulation is employed to study the thermal transport in two-directional (2-D) random fibres. Satisfactory agreement with existing data validates the numerical model. The dimensionless effective thermal conductivity (ETC) of the porous fibres increases with the solder joint sizes. As the solder joint size (i.e., solder joint ratio) increases by 3.06%, the in-plane (k_e-in) and out-of-plane (k_e-out) dimensionless ETC increase by 9.0% and 437.2%, respectively. However, the solder joint skips will weaken the thermal conductivity of the fibres. For the same fibre, the ETC of the fibre increases as the thermal conductivity of solders increases. Further, when the dissimilarity in thermal conductivity between the filling medium and the fibre is reduced, the fibre is less affected by the solder joint skips. Finally, it should be supplemented that the in-plane and out-of-plane ETC (k_e-in and k_e-out) of the fibre without any solder joint are reduced by an average of 14.3% and 98.8%, respectively.