The two charge-density wave (CDW) transitions in NbSe3 were investigated by scanning tunneling microscopy (STM) on an in situ cleaved (b, c) plane. The temperature dependence of first-order CDW satellite spots, obtained from the Fourier transform of the STM images, was measured between 5 and 140 K to extract the surface critical temperatures (T{s}). The low-T CDW transition occurs at T{2s}=70-75 K, more than 15 K above the bulk T{2b}=59 K while at exactly the same wave number. A plausible mechanism for such an unusually high surface enhancement is a softening of transverse phonon modes involved in the CDW formation. The regime of 2D fluctuations is analyzed according to a Berezinskii-Kosterlitz-Thouless type of surface transition, expected for this incommensurate 2D CDW, by extracting the temperature dependence of the order parameter correlation functions.