The paper analyzes the results of experimental investigations into the laser beam propagation under conditions of developed convective turbulence over a heated surface with the Rayleigh number Ra ~ 108 - 1010. The laser beam (l= 0.63 mm) propagated at the height of 18, 25, and 36 cm above the surface. The path length was 2 m. The transmitter optical system generated a plane wave with the Gaussian intensity distribution. Laser beam displacements along the horizontal and vertical coordinates were measured simultaneously. The variance of displacements sa2, the correlation function b(t), and the spectral density of fluctuations fW(f) were calculated. The dependence of fluctuations of the image centroid on the detector diameter was determined at different heights above the surface.