The measurements of resistivity and low-field Hall effect made in the temperature range 3.3-295 K have been used to investigate the transport properties of modulation-doped, lattice-matched In0.53Ga0.47As/In0.52Al0.48As heterojunctions as a function of the spacer thickness in the range from 0 to 400 Angstrom. It is found that the sheet carrier density determined at temperatures below about 80 K decreases rapidly with increasing spacer thickness. The low-temperature Hall mobility increases substantially when increasing the spacer thickness from 0 to 100 Angstrom, and decreases gradually with further increase in spacer thickness. The results suggest that, in addition to alloy scattering, remote ionized-impurity scattering is a major scattering mechanism at low temperatures in the samples with thin spacer layer and that background impurity scattering prevails in the samples with spacer thickness larger than about 100 A. The effect of modulation doping on the mobility decreases progressively with increasing temperature: the electron mobility becomes practically independent of spacer thickness in the temperature range above about 200 K. The variation of Hall mobility with temperature in the range above 90 K has been used to determine the energy of longitudinal optical phonons that limit the mobility of electrons at high temperatures.