Understanding heat dissipation processes at nanoscale during cellular thermogenesis is essential to clarify the relationships between the heat and biological processes in cells and organisms. A key parameter determining the heat flux inside a cell is the local thermal conductivity, a factor poorly investigated both experimentally and theoretically. Here, using a nanoheater/nanothermometer hybrid based on a polydopamine shell encapsulating a fluorescent diamond nanocrystal, we measured the intracellular thermal conductivity of HeLa cell with a spatial resolution of about 200 nm. Its mean value of 0.11 Wm -1 K -1 determined for the first time is significantly smaller than that of water. Bayesian analysis of the data strongly supports the existence of variation of the intracellular thermal conductivity of about 40%. These results present a major milestone towards understanding the intracellular heat transfer phenomena at nanoscale.