In the heat treatment processes, offline utilization of first-principles models is well-established. These models tend to be complex, computationally demanding, and rely heavily on empirical relations. The fidelity of these models degrades over time due to changes in the process resulting in plant-model mismatch, which is typically attributed to an incorrect constitutive relation of a physical mechanism in the model (i.e. fouling in the heat exchangers). In this paper, we propose two hybrid modeling approaches, namely Sparse Identification of Nonlinear Dynamics with Control and least square estimation, to learn the dynamics of the discrepancy between the measurement data and the simulation model. The hybrid modeling approach is implemented on a heat exchanger network (HEN) example and it is shown that the accuracy of the first principles dynamic model is improved.