The efficient design of domestic refrigeration systems is crucial to reduce the high energy consumption. To this aim, a numerical study of the air circulation and heat transfer in fluid and between fluid and solids in a refrigerator was conducted at the full order level using the Conjugated Heat Transfer (CHT) method [1,2] to investigate the temperature distribution and flow pattern inside a fridge. This study aimed to examine both natural and forced convection-based models of a fridge. The model is founded on the principles of mass, momentum, and energy conservation. The flow was considered to be incompressible and the buoyancy terms were modeled based on the Boussinesq approximation. The governing set of partial differential equations was solved using the finite volume method and an iterative procedure. A parametric study was carried out considering factors such as the ambient temperature, fridge fan velocity, and evaporator temperature. To reduce the computational cost of the full order problem, a non-intrusive reduced order model was developed using the Proper Orthogonal Decomposition with Interpolation (PODI) method [3]. This approach aimed to determine the temperature and flow field at a specific parametric location. The Gappy POD (GPOD) method [4] was used to reconstruct the full temperature field using data obtained from a limited number of sparse sensor locations. The accuracy of the temperature reconstruction was improved by several orders when compared to the GPOD method if the sensor locations were optimally selected using the Discrete Empirical Interpolation Method (DEIM) [5]. The full order model was validated against experimental results, and the errors associated with various reduced order methods were compared to benchmark numerical results.