Computing diagnoses in domains with continuously changing data is a difficult, but essential aspect of solving many problems. To address this task, this paper describes a dynamic influence diagram (ID) construction and updating system, DYNASTY, and its application to constructing a decision-theoretic model to diagnose acute abdominal pain, a domain in which the findings evolve during the diagnostic process. For a system which evolves over time, DYNASTY constructs a parsimonious ID, and then dynamically updates the ID, rather than constructing a new network from scratch for every time interval. In addition, DYNASTY contains algorithms for testing the sensitivity of the constructed network's system parameters. The main contributions of this paper are: (1) presenting an efficient temporal influence diagram technique based on parsimonious model construction; and (2) formalizing the principles underlying a diagnostic tool for acute abdominal pain which explicitly models time-varying findings.