Thermal processing has long been known and employed for atomic and molecular materials, but has been elusive in colloidal materials because of a lack of colloidal systems with easily controlled temperature-responsive behavior, as well as a dearth of fundamental understanding for how the thermal history influences the development and arrest of structural morphologies and features in these systems. In this project, these challenges will be overcome using newly developed thermoresponsive colloids, and large-scale simulations and experiments that can rapidly probe the multitude of possible thermal histories and structures that emerge from them. Experiments and simulation will be combined to characterize how kinetic trajectories in thermodynamic variables map onto the relevant descriptors of emergent structural correlations and material properties including rheology. Leading efforts will establish categorical behavior for quenches in the homogeneous fluid phase, as well as in both metastable (binodal) and unstable (spinodal) regions of phase coexistence, followed on by more complex quenches involving annealing in more than one of these regions to seek out novel structures and rheology. Doing so will enable a more fundamental understanding for how kinetic processes of gelation, phase separation and glass formation compete in colloidal fluids to initiate, evolve and eventually arrest structure, and how the features of the arrested structure control the linear and non-linear mechanics of the material. This fundamental understanding will be used to develop a new conceptual framework for using thermal processing to design and engineer colloidal materials with well-specified structure and properties.