We report a new approach to controllable thermal stimulation of a single living cell and its compartments. The technique is based on the use of a single polycrystalline diamond particle containing silicon-vacancy (SiV) color centers. Due to the presence of amorphous carbon at its intercrystalline boundaries, such a particle is an efficient light absorber and becomes a local heat source when illuminated by a laser. Furthermore, the temperature of such a local heater is tracked by the spectral shift of the zero-phonon line of SiV centers. Thus, the diamond particle acts simultaneously as a heater and a thermometer. In the current work, we demonstrate the ability of such a Diamond Heater-Thermometer (DHT) to locally alter the temperature, one of the numerous parameters that play a decisive role for the living organisms at the nanoscale. In particular, we show that the local heating of 11-12 degrees C relative to the ambient temperature (22 degrees C) next to individual HeLa cells and neurons, isolated from the mouse hippocampus, leads to a change in the intracellular distribution of the concentration of free calcium ions. For individual HeLa cells, a long-term (about 30 s) increase in the integral intensity of Fluo-4 NW fluorescence by about three times is observed, which characterizes an increase in the Ca2+ concentration of free calcium in the cytoplasm. Heating near mouse hippocampal neurons also caused a calcium surge-an increase in the intensity of Fluo-4 NW fluorescence by 30% and a duration of similar to 0.4 ms.