Numerous studies have focused on constructing multimodal machine learning models for estimating a person's cognitive load. However, a prevalent limitation is that these models are typically evaluated on data from the same scenario they were trained on. Little attention has been given to their robustness against data distribution shifts, which may occur during deployment. The aim of this paper is to investigate the performance of these models when confronted with a scenario different from the one on which they were trained. For this evaluation, we utilized a dataset encompassing two distinct scenarios: an n-Back test and a driving simulation. We selected a variety of classic machine learning and deep learning architectures, which were further complemented by various fusion techniques. The models were trained on the data from the n-Back task and tested on both scenarios to evaluate their predictive performance. However, the predictive performance alone may not lead to a trustworthy model. Therefore, we looked at the uncertainty estimates of these models. By leveraging these estimates, we can reduce misclassification by resorting to alternative measures in situations of high uncertainty. The findings indicate that late fusion produces stable classification results across the examined models for both scenarios, enhancing robustness compared to feature-based fusion methods. Although a simple logistic regression tends to provide the best predictive performance for n-Back, this is not always the case if the data distribution is shifted. Finally, the predictive performance of individual modalities differs significantly between the two scenarios. This research provides insights into the capabilities and limitations of multimodal machine learning models in handling distribution shifts and identifies which approaches may potentially be suitable for achieving robust results.