Throughout their lifecycle, structures undergo changes in material properties due to various factors such as damage, corrosion, or fatigue. Therefore, in order to capture and locate the changes, it is important to construct high-fidelity digital representations that evolve alongside physical structures. This is further enabled by abundantly available sensors, the growing sophistication of sensor technology and numerical simulation techniques. Some of these tasks need to be treated as coupled field problems, such as thermo-mechanical systems. Therefore, the digital twins of these must account for the interaction between multiple domains, including temperature (and other environmental effects’) fields and mechanical fields. A key step in digital twinning is system identification, which involves determining the current state of the structure, such as the material properties and localizing damages/weaknesses. This work focuses on solving an inverse problem to identify both temperature and damage (now modelled by a change in the distribution of Young's modulus) within a structure. The optimization problem is formulated to minimize the discrepancy between the measured and the simulated displacements and strains at multiple sensor locations. The cost function uses a p-norm aggregation technique to weight contributions from different sensors more effectively. We investigate two approaches to this coupled identification problem: sequential identification, where temperatures and damages are identified separately, and simultaneous identification, where both fields are identified together. To regularize the minimization problem, smoothing techniques such as vertex morphing are applied, ensuring robustness and preventing overfitting. Several optimization algorithms are explored and evaluated on 2D and 3D structural examples, compared against the standard steepest descent method. This study demonstrates the potential for high-fidelity digital twins in accurately capturing the coupled thermal and mechanical behavior of structures, providing also insights into the relative comparison of sequential versus simultaneous coupled field system identification.