This paper analyzes solar wind power spectra of bulk and thermal speed fluctuations that are computed with a time resolution of 32 ms in the frequency range of 0.001–2 Hz. The analysis uses measurements of the Bright Monitor of the Solar Wind on board the Spektr-R spacecraft that are limited to 570 km s−1 bulk speed. The statistics, based on more than 42,000 individual spectra, show that: (1) the spectra of bulk and thermal speeds can be fitted by two power-law segments; (2) despite their large variations, the parameters characterizing frequency spectrum fits computed on each particular time interval are very similar for both quantities; (3) the median slopes of the bulk and thermal speeds of the segment attributed to the MHD scale are −1.43 and −1.38, respectively, whereas they are −3.08 and −2.43 in the kinetic range; (4) the kinetic range slopes of bulk and thermal speed spectra become equal when either the ion density or magnetic field strength are high; (5) the break between MHD and kinetic scales seems to be controlled by the ion β parameter; (6) the best scaling parameter for bulk and thermal speed variations is a sum of the inertial length and proton thermal gyroradius; and (7) the above conclusions can be applied to the density variations if the background magnetic field is very low.