The viscosity of gel-forming fluids is notoriously complex and its study can benefit from new model systems that enable a detailed control of the network features. Here we use a novel and simple microfluidic-based active microrheology approach to study the transition from Newtonian to non-Newtonian behavior in a DNA hydrogel whose structure, connectivity, density of bonds, bond energy and kinetics are strongly temperature dependent and well known. In a temperature range of 15 °C, the system reversibly and continuously transforms from a Newtonian dispersion of low-valence nanocolloids into a strongly shear-thinning fluid, passing through a set of intermediate states where it behaves as a power-law fluid. We demonstrate that the knowledge of network topology and bond free energy enables to quantitatively predict the observed behavior using established rheology models.