We propose a novel material prepared by microwave-hydrothermal treatment, the tetragonal xenotime-type yttrium orthophosphate YPO4 nanocrystals doped by different concentrations of Dy3+. It may be suitable for laser-induced local heating of cancer tumors for hyperthermia. We heated a powder consisted of the nanoparticles by focused quasi-CW laser irradiation at different wavelengths in the near IR spectral range fitting the transparency window of biological tissues. The local temperature on the surface of the powder in the place of irradiation increases linearly with increasing laser power and increasing the Dy3+ concentration. At the same time the efficiency of local heating Φ = ΔT /(Pf), (ΔT is a local temperature increase, f is an oscillator strength of absorption transition, and P is the quantity of laser power) is proportional to the energy of the initially excited electronic level. The proposed method allows for high rates of heating and cooling. The laser power used for heating was rather low, tens of milliwatts that together with short heating time to required temperature may result in extremely low doses of laser irradiation for heating.