Modelling execution times in complex real-time embedded systems is vital for understanding and predicting tasks' temporal behaviour, and to improve the system scheduling performance. Previous research mainly relied on worst-case execution time estimations based on formal static analyses that are often pessimistic. The models that resulted are hard to maintain and even harder to validate. In this work, the novel use of Digital Twins provides opportunities to improve this issue and beyond for dependable real-time systems. We aim to establish and contribute to three questions: (i) how to easily model execution times with an adequate level of abstraction, and how to evaluate the quality of that model; (ii) how to identify errors in the models and how to evaluate the impact of errors; and (iii) how to make decisions as to when and how to improve the models. In this paper, we proposed a Digital Twin-based adaptation framework, and demonstrated its use for modelling and refining execution time profiles. Key decisions concerning the quality of the model and its impact on performance are evaluated. Finally, some challenges and key research questions for the formal method community are proposed.