He-3 crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To find out the reason for this discrepancy, we have performed the first quantitative investigation on the growth dynamics of the faceted and rough surfaces of He-3 crystals in the temperature range of 60-110 mK. We have applied an original method to obtain the variation of the overpressure on the crystal surface by measuring its curvature and height locally using a Fabry-Perot interferometer. The growth of the rough surface was found to be limited by the transport of the latent heat which elaborates in the liquid, in accordance with theoretical predictions (Puech L., et al. in J. Low Temp. Phys. 62:315, 1986; Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990) and previous measurements near the minimum of the melting curve (Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990). The mobility of an elementary step on a facet was shown to be limited by the latent heat transport as well. The values obtained for the step free energy are by two orders of magnitude smaller than at ultra low temperatures, which we show to be the result of quantum oscillations of the solid-liquid interface, which quickly become damped when temperature decreases below 100 mK.