Optimizing and monitoring the growth conditions of Pt films, often used as bottom electrodes in multiferroic material systems, represents a highly relevant issue that is of importance for controlling the crystalline quality and performance of ferroelectric oxides such as, e.g. LuFeO3. We performed a time-resolved monitoring of the growth and morphology of Pt films during pulsed laser deposition (PLD) in dependence on the grown film effective thickness and on the growth temperature Tg using in situ grazing incidence small-angle X-ray scattering (GISAXS). Through real-time analysis and modeling of GISAXS patterns, we could fully characterize the influence of Tg on the morphology and on the growth kinetics of the Pt layers. Consequently, critical and characteristic effective thicknesses for the transitions nucleation phase (I)/coalescence phase (II) and coalescence phase (II)/coarsening phase (III) could be determined. In combination with complementary microscopic imaging and chemical mapping via combined SEM/EDXS, we demonstrate the occurrence of a morphological progression in the Pt PLD-grown Pt films, changing from grains at room temperature to a 3D-island morphology at 300 degrees C, further to a hole-free structure at 500 degrees C, and finally to a channel structure for 700 and 900 degrees C. The film topography, as characterized by atomic force microscopy (AFM), favors the PLD growth of Pt layers at temperatures beyond 700 degrees C where the film is homogeneous, continuous, and hole-free with a flat and smooth surface. The double dependency of the percolation transition on the film effective thickness and on the growth temperature has been established by measuring the electrical conductivity.