This article contributes to a special session on the Hyperfast Switching Peltier Cooling System Benchmark. The CAPTAIN Toolbox is utilised to identify statistical models for the system. The article focuses on a 'data-based' estimation of multi-input, single-output linear transfer function models for the chamber temperature. These models are decomposed into three subsystems, to yield a similar structural form to the physical apparatus. Hence, in a limited manner, the approach can be used to predict the intermediate flow rate and Peltier temperature variables. However, the decomposed models are technically not identifiable without reference to the validation data. Finally, the article briefly discusses the application of time variable parameter models.