Although delayed detonation models of thermonuclear explosions of white dwarfs seem promising for reproducing Type Ia supernovae, the transition of the flame propagation mode from subsonic deflagration to supersonic detonation remains hypothetical. A potential instant for this transition to occur is the onset of the distributed burning regime, i.e., the moment when turbulence first affects the internal flame structure. Some studies of the burning microphysics indicate that a deflagration-to-detonation transition may be possible here, provided the turbulent intensities are strong enough. Consequently, the magnitude of turbulent velocity fluctuations generated by the deflagration flame is analyzed at the onset of the distributed burning regime in several three-dimensional simulations of deflagrations in thermonuclear supernovae. It is shown that the corresponding probability density functions fall off toward high turbulent velocity fluctuations much more slowly than a Gaussian distribution. Thus, values claimed to be necessary for triggering a detonation are likely to be found in sufficiently large patches of the flame. Although the microphysical evolution of the burning is not followed and a successful deflagration-to-detonation transition cannot be guaranteed from simulations presented here, the results still indicate that such events may be possible in Type Ia supernova explosions.