Nanoemulsions are widely used in applications such as food products, cosmetics, pharmaceuticals, and enhanced oil recovery for which the ability to engineer material properties is desirable. Moreover, nanoemulsions are emergent model colloidal systems because of the ease in synthesizing monodisperse samples, flexibility in formulations, and tunable material properties. In this work, we study a nanoemulsion system previously developed by our group in which gelation occurs through thermally induced polymer bridging of droplets. We show here that the same system can undergo a sol-gel transition at room temperature through the addition of salt, which screens the electrostatic interaction and allows the system to assemble via depletion attraction. We systematically study how the addition of salt followed by a temperature jump can influence the resulting microstructures and rheological properties of the nanoemulsion system. We show that the salt-induced gel at room temperature can dramatically restructure when the temperature is suddenly increased and achieves a different gelled state. Our results offer a route to control the material properties of an attractive colloidal system by carefully tuning the interparticle potentials and sequentially triggering the colloidal self-assembly. The control and understanding of the material properties can be used for designing hierarchically structured hydrogels and complex colloid-based materials for advanced applications.