A study on the dependence of the thermal conductivity of the percolation network of carbon nanotubes (or CNTs) on the type and degree of functionalization has been carried out. The study was focused on the influence of the more commonly used -COOH, -OH and -СОNH2 groups. A non-linear dependence of the conductivity on the number of functional groups has been revealed. A small number of functional groups can improve conductivity, and a large one can impair it. We presuppose the existence of competing processes that increase thermal conductivity (changes in the CNT geometry, improvement of the contact between them) and enhance photon scattering (emergence of defects and scattering centers). The data can be used for controlling the thermophysical properties of the CNTs as well as determining the optimal degree of functionalization during the development of composites and nanodevices.