## 1 Introduction
For example, in [16], the authors indicate that the heat capacity \(C\) of the sample may be easily calculated with the given mass m of the sample and its specific heat value \(C_{s}\) according to Formula (1), whilst the thermal resistance requires special estimation algorithms. \[C=C_{s}m \tag{1}\]  
The heat capacity of other model's elements of defined mass and specific heat can also be estimated using (1). However, in order to obtain highly accurate, detailed calibration is necessary. This can be achieved using an excitation input signal from a power-controlled heat source. The analysis of heat flow in non-adiabatic calorimeters with different levels of complexity has been previously proposed and compared in several studies. For instance, a detailed approach to the transient analysis of equivalent circuits for various thermal systems has been presented in [22; 23; 24]. Multiparameter thermo-electric equivalent circuits have also been used to model heat sinks and thermal sources [25; 26], as well as lithium-ion batteries in [27; 28; 29; 30]. Additionally, several authors have developed a nonlinear RC-thermal circuit with variable thermal resistance [31]. Examples of lumped-parameter thermal modeling in various applications can be found in [32; 33; 34; 35; 36; 37]. In particular, a lumped-element equivalent RC circuit with multisensory simultaneous measurements for the thermal identification of the examined apparatus was proposed in [38]  
Thermal modeling using lumped-parameter thermal networks is associated with uncertainty regarding the power loss model and the computational complexity of identifying the model using global optimization. To address these challenges, data-driven nonlinear function approximation using supervised machine learning has been proposed in [39; 40]. In this paper, an equivalent thermo-electric circuit (equivalent thermal network) is proposed for a non-adiabatic measurement system designed to perform thermal power measurements of nanoparticles exposed to an alternating magnetic field. In our RC lumped-element model, apart from the parameters included in the simplest non-adiabatic corrected-slope method, such as the heat capacity of the nanoparticle sample and its thermal resistance to the surroundings, we also consider other factors affecting the measurement error, based on findings from other studies. For example, [PERSON] et al. [41] noted that different levels of insulation in the closest surroundings of the non-adiabatic system lead to varying heating time curves. Therefore, the thermal properties of the sample's closest environment must be considered in the corrected-slope formula to accurately determine the heating power of the sample. To address this issue, we modeled the thermal resistivity and capacity of the surrounding environment using additional RC lumped elements. A similar model incorporating these parameters into a set of differential equations describing heat flow in the system can be found in [42; 43]. One publication [38] presents an approach where the authors used a lumped-element model to describe the sample's immediate environment, but specifically in a differential calorimeter setup. In our measurement setup, magnetic nanoparticles were heated by a strong alternating magnetic field generated by a large current flow through the excitation coil. Such a large current driven through the resistive wires of the coil also created heat, resulting in a substantial temperature rise in the carcass and its surroundings. A specially adapted cooling system for the excitation coil was used to reduce this effect significantly. However, if the efficiency of the cooling system is insufficient to drain all of the dissipated energy, some heat may still be transferred to the sample and its surroundings, resulting in an overestimation of the input power [44]. This is particularly important if the nanoparticle heating efficiency is low compared to the external heat flow, just like it was in our case.