Thermally conductive polymer composites offer new possibilities for replacing metal parts in several applications (for example generators, electric motors and heat exchangers). Nanotechnology is a potential technology that would enable the development of polymer materials with properties. It is considered that the improvement in thermal conductivity of the polymer could be accomplished by the addition of highly conductive nanofillers in the polymer matrix. The most commonly used nanofillers are carbon nanotubes (CNT). The objective of this study was to determine the effect of the addition of multi-walled carbon nanotubes (MWCNT) to the thermal conductivity of polylactide acid (PLA), the influence of the sample thickness on the thermal conductivity of the PLA + MWCNT system, the influence of the MWCNT COOH and COOC12H25 groups on the thermal conductivity of PLA + MWCNT and the influence of the polyethylene matrix on the thermal conductivity of PE + MWCNT. The heat conductivity was measured by using the Transient Hot Bridge. The research results have shown that the thickness of the sample does not significantly affect the thermal conductivity of the PLA + MWCNT system. The thermal conductivity of the PLA + MWCNT system suggests that the addition of carbon nanotubes in 4% mass causes an increase in thermal conductivity by approximately 80%. Measuring the thermal conductivity of PLA + MWCNT-COOH and PLA + MWCNT-COOC12H25 showed that there was no significant difference in thermal conductivity caused by the functionalization of MWCNT. The results of the polyethylene matrix influence on thermal conductivity show that PE-HD has a significantly higher thermal conductivity and a significantly higher increase in thermal conductivity by adding MWCNT than PE-LD. The increase in thermal conductivity of the system with the PLA matrix is considerably higher than the observed increase in the PE matrix system.