Despite improved sensitivity of nanothermometers, direct observation of heat transport inside single cells has remained challenging for the lack of high-speed temperature imaging techniques. Here, we identified insufficient temperature resolution under short signal integration time and slow sensor kinetics as two major bottlenecks. To overcome the limitations, we developed B-gTEMP, a nanothermometer based on the tandem fusion of mNeonGreen and tdTomato fluorescent proteins. We visualized the propagation of heat inside intracellular space by tracking the temporal variation of local temperature at a time resolution of 155 mus and a temperature resolution 0.042 degrees C. By comparing the fast in situ temperature dynamics with computer-simulated heat diffusion, we estimated the thermal diffusivity of live HeLa cells. The present thermal diffusivity in cells was about 1/5.3 of that of water and much smaller than the values reported for bulk tissues, which may account for observations of heterogeneous intracellular temperature distributions.