The publication explores the applicability of implicit multilinear model approaches in air conditioning systems. Implicit multilinear time-invariant models offer a structure that allows for the representation of most of the fundamental physical equations of HVAC systems. Since the implicit multilinear time-invariant model class is closed, it enables a component-based modeling approach to represent various types of HVAC systems with different combinations of components. Multilinear time-invariant models are usually represented by tensors. With HVAC-Systems having a large number of inputs and states, the models can be efficiently represented in a decomposed manner, resulting in a matrix representation. As an example, the model of a precision climatization hutch with a PI controller is derived and simulated.