The requirements for accurate numerical simulations are increasing steadily. Modern high precision physics experiments now exceed the achievable numerical accuracy of standard commercial and scientific simulation tools. One example are optical resonators for which changes in the optical length are now commonly measured to 10-15 precision. The achievable measurement accuracy for resonators and cavities is directly influenced by changes in the distances between the optical components. If deformations in the range of 10-15 occur, those effects cannot be modeled and analyzed anymore with standard methods based on double precision data types. New experimental approaches point out that the achievable experimental accuracies may improve up to the level of 10-17 in the near future. For the development and improvement of high precision resonators and the analysis of experimental data, new methods have to be developed which enable the needed level of simulation accuracy. Therefore we plan the development of new high precision algorithms for the simulation and modeling of thermo-mechanical effects with an achievable accuracy of 10-20. In this paper we analyze a test case and identify the problems on the way to this goal.