A method for the determination of the thermal conductivity of polymer composite materials by using Co-based ferromagnetic microwires is proposed. Microwire segments were integrated into the samples of studied materials during their manufacture and used as current microheaters and resistance thermometers. As a representative material, we used a material based on nitrile butadiene rubber filled with hexagonal boron nitride after its low-temperature carbonization and a significant increase in thermal conductivity. The thermal conductivity values of composite samples determined during experiments varied from 1.0 W/(m·K) to 1.8 W/(m·K) depending on the percentage of boron nitride. The thermal conductivity values obtained are in good agreement with the estimates obtained by the standard laser flash method.