###### Abstract
1D models usually neglect the interface thermal conduction and require the use of a heat-transfer coefficient between the fluid and the solid matrix. Despite the larger computational cost, 2D models have also been considered, mainly used when dealing with slow heat transfer processes along the perpendicular flow direction, where the modelled fluid cannot transport the heat completely within one cycle [16]. Regarding the 3D models developed so far, the computational resources were so high that in order to model a complete MC regenerator, [PERSON] et al. (2009), only computed a few magnetocaloric cycles [17]. In other cases, authors adopt different strategies to reduce the computing power cost, required by the designed models. For example [PERSON] et al. (2016) only modelled one MC microchannel regenerator instead of a complete structure [18]. [PERSON] et al. (2018) divided the model into two so that the fluid dynamics (3D) could be computed separately from the heat transfer process (1D) [19]. [PERSON] et al. (2021) compiled several published MC numerical models, classifying them by the degree to which the underlying physical phenomena are solved and implemented [20]. Each physical property used in MC models depends on parameters like temperature \(T\) and magnetic field \(H\). In MCM numerical modelling, the use of these two dependencies in the literature presents itself considerably divergent. Recent models all use temperature dependent specific heat (\(C_{p}(T)\)) domains, whether it has been calculated through Mean Field Theory (MFT) or obtained experimentally [21; 22; 23]. \(C_{p}(T)\) is required to have a thermodynamic sound model [24]. Nevertheless, some models have used a constant \(C_{p}\) approximations [25; 26]. These intrinsic thermal properties, like \(C_{p}\) and \(k\) are in the genesis of specific energy transfer mechanisms. To more accurately evaluate the overall contributions to heat transfer, \(C_{p}\) and \(k\) temperature dependence should be accounted for in numerical simulations [27], not only because it is a closer representation of actual physical conditions but also to provide better predictive solutions. Concerning thermal conductivity \(k\), [PERSON] et al. (2012) demonstrated that large operating frequencies demand large \(k\), and small operating frequencies demand small \(k\), when simulating a complete AMR regenerator [28]. So far, [PERSON] et al. (2019) developed the only AMR numerical model that employs temperature dependent \(k\)[29]. The research group concluded that changing \(k\) approximately by 50% within a temperature window of 10 K, can significantly impact the overall AMR cycle's performance. This result may be approximated to actual values in some cases since [PERSON] et al. (2004) already had measured a 10% change in thermal conductivity across a 20 K window near room temperature for some MC materials [30], which can influence the time constant temperature change during the MCE [31]. Despite that, nowadays, predictive algorithms already can provide reliable and accurate MCM \(C_{p}(T)\) input values [32], the same cannot be said for the material's \(k\), which is still considered immutable [33; 34; 35; 23]. As pointed out in this introduction, plenty of AMR numerical models have been developed in the past. However, the accuracy of these models can be improved by considering temperature dependent properties. [PERSON] et al. (2019) successfully incorporated \(k(T)\) values into a magnetocaloric device model [29]. Nevertheless, in this paper, a deeper scrutiny is made on the heat transfer dynamics of a idealized MCM slab, detailing the impact of implementing more than one temperature dependent physical property. The main objective is to fill a gap in the literature by understanding specifically how the inclusion of \(C_{p}(T)\) and \(k(T)\), in a completely controlled numerical environment, can influence the heat transfer process, highlighting the relevance of the thermal conductivity's temperature dependence on magnetocaloric materials.