Many chemical and biological reactions, including ligand exchange processes, require thermal energy for the reactants to overcome a transition barrier and reach the product state. Temperature-jump (T-jump) spectroscopy uses a near-infrared (NIR) pulse to rapidly heat a sample, offering an approach for triggering these processes and directly accessing thermally-activated pathways. However, thermal activation inherently increases the disorder of the system under study and, as a consequence, can make quantitative interpretations of structural changes challenging. In this Article, we optimise a deep neural network (DNN) for the instantaneous prediction of Co K-edge X-ray absorption near-edge structure (XANES) spectra. We apply our DNN to analyse T-jump pump/X-ray probe data pertaining to the ligand exchange processes and solvation dynamics of Co2+ in chlorinated aqueous solution. Our analysis is greatly facilitated by machine learning, as our DNN is able to predict quickly and cost-effectively the XANES spectra of thousands of geometric configurations sampled from ab initio molecular dynamics (MD) using nothing more than the local geometric environment around the X-ray absorption site. We identify directly the structural changes following the T-jump, which are dominated by sample heating and a commensurate increase in the Debye-Waller factor.