We present a theoretical study of the transport properties of two-dimensional hole gas (2DHG) in Ge channel modulation-doped square quantum wells, with very high room-temperature drift mobilities. Within the variational approach, we obtain analytic expressions for the carrier distribution, and autocorrelation functions for various scattering mechanisms. The results were used to determine the hole mobility where only the relevant scattering processes, namely acoustic phonons (Deformation potential and Piezoelectric coupling), ionized impurity, surface roughness were considered. The partials and total mobility dependences on temperature were found. It is shown that acoustic phonon and surface roughness scattering are the dominant mechanism. The interpretation of these results is carried out and the scattering mechanisms limiting the 2DHG mobility in Ge quantum wells of SiGe heterostructure are discussed.