The thermal conductivity k and resistivity ρ of biocarbon matrices, prepared by carbonizing medium-density fiberboard at T carb = 850 and 1500°C in the presence of a Ni-based catalyst (samples MDF-C(Ni)) and without a catalyst (samples MDF-C), have been measured for the first time in the temperature range of 5-300 K. X-ray diffraction analysis has revealed that the bulk graphite phase arises only at T carb = 1500°C. It has been shown that the temperature dependences of the thermal conductivity of samples MDF-C-850 and MDF-C-850(Ni) in the range of 80-300 K are to each other and follow the law of k(T) ~ T 1.65 , but the use of the Ni-catalyst leads to an increase in the thermal conductivity by a factor of approximately 1.5, due to the formation of a greater fraction of the nanocrystalline phase in the presence of the Ni-catalyst at T carb = 850°C. In biocarbon MDF-C-1500 prepared without a catalyst, the dependence is k(T) ~ T 1.65 , and it is controlled by the nanocrystalline phase. In MDF-C-1500(Ni), the bulk graphite phase formed increases the thermal conductivity by a factor of 1.5-2 compared to the thermal conductivity of MDF-C-1500 in the entire temperature range of 5-300 K; k(T = 300 K) reaches the values of ~10 W m-1 K-1 , characteristic of biocarbon obtained without a catalyst only at high temperatures of T carb = 2400°C. It has been shown that MDF-C-1500(Ni) in the temperature range of 40-300 K is characterized by the dependence, k(T) ~ T 1.3 , which can be described in terms of the model of partially graphitized biocarbon as a composite of an amorphous matrix with spherical inclusions of the graphite phase.