One of the key challenges to model condition monitoring is; how to suitable match the level of detail of the model description of the diagnostic requirements. To do so, a counter-current heat exchanger of the tire factory was investigated. Moreover, a two-stage grey-box modelling was deployed. The modelling is deployed in a discrete state space, relying on a combination of prior knowledge, along with the recorded data. The nonlinear model structure of heat exchanger is derived considering the use of the prior knowledge; thereby, it is converted into linearized form. The discretization of the linearized model is applied. The optimization procedure based on recorded data is adopted to estimate the unknown physical parameters in state space system matrices. The well-known N4SID subspace identification method is used to compare the obtained results.