The antagonistic effect of processing and thermal annealing on both the filler structure and the polymer matrix is explored in polymer nanocomposites based on natural rubber with precipitated silica incorporated by coagulation from aqueous suspension followed by roll-milling. Their structure and linear and non-linear rheology have been studied, with a particular emphasis on the effect of high temperature thermal treatment and the number of milling passes. Small-angle X-ray scattering intensities show that the silica is organized in small, unbreakable aggregates containing ca. 50 primary nanoparticles, which are reorganized on a larger scale in filler networks percolating at the highest silica contents. As expected, the filler network structure is found to be sensitive to milling, more milling inducing rupture, as evidenced by the decreasing Payne effect. After thermal treatment, the nanocomposite structure is found to be rejuvenated, erasing the effect of the previous milling on the low-strain modulus. In parallel, the dynamics of the samples described by the rheology or the calorimetric glass-transition temperature remain unchanged, whereas the natural latex polymer network structure is modified by milling towards a more fluid-like rheology, and cannot be recovered.