Wind tunnel experiments with rocket fin edges aim, among other things, to examine how fin edge geometries change under thermal loads, such as those occurring during re-entry. Currently, these geometry changes are evaluated by comparing measurements of the test specimen before and after the experiment. Extending the available evaluation options, we propose a continuous observation of the thermal deformation through neural three-dimensional geometry reconstruction. Neural reconstruction approaches learn object geometry from a dataset of multi-view images and corresponding camera poses. High surface smoothness in the reconstructed geometries is a desirable property for further studies, e.g. for computational fluid dynamics simulations. The NeuS method aims to produce smooth surfaces by representing them as the zero-level set of a learned signed distance function. In order to assess the applicability of NeuS to our specific reconstruction problem, we test the approach on synthetic data generated to resemble recordings from wind tunnel experiments. In these synthetic datasets, we vary scene and camera parameters such as number of viewpoints or uncertainty in camera poses and evaluate their influence on the reconstruction performance. The results of this parameter study provide recommendations for data acquisition in wind tunnel experiments to optimise reconstruction performance. Since NeuS is originally designed for the reconstruction of static scenes, we incorporate a dynamic approach that allows the method to be used on time-dependent data, suitable for the temporally evolving video sequences from our use case. Using a synthetically created animation with the same duration and frame rate as a real video sequence, we show that the proposed dynamic approach leads to a successful reconstruction within a feasible runtime and therefore provide a proof of concept for its application in wind tunnel experiments.