## 1 Introduction  
Magnetic nanoparticles have been extensively researched due to their potential use in various medical applications, including anti-cancer hyperthermia treatment [1, 2], medical imaging [3, 4], and theranostics [5, 6, 7]. The therapeutic effect of hyperthermia is based on increasing the temperature of tumor tissues, typically to around 40-43 \({}^{\circ}\)C [8]. In this temperature range, cancerous cells are killed by inducing programmed cell death, which is called apoptosis [9]. The primary goal of nanoparticle application in hyperthermia is to maximize the power deposition inside the tumor's tissue. The iron mass-normalized specific absorption rate (SAR) is the physical quantity commonly used for evaluating the nanoparticle heating efficiency when subjected to alternating magnetic fields [10]. An accurate determination of SAR is crucial for quantifying the ability of superparamagneticnanoparticles (SPIONs) to generate heat during AC magnetization [11]. Adiabatic conditions are most preferred for precise SAR measurements [12]. However, experimental analysis in alternating magnetic fields requires a unique calorimeter design composed of nonmagnetic materials, which may not guarantee perfect thermal isolation. We built a hybrid system for SAR measurement using both AC magnetometry and calorimetry, as presented in [13; 14]. The application of an ideal calorimetric model did not achieve acceptable compliance between the two methods. The measured heating curves poorly fit the theoretical adiabatic curves. In such a case, non-adiabatic conditions must be considered to avoid significant errors. Non-ideal calorimeter measurements require extended analysis, in which more specific parameters like the examined sample's thermal resistance or heat capacity need to be considered to properly model the undesired outward heat flow from the sample to the environment [15]. Several approaches have already been proposed by different authors to describe the non-adiabatic behavior of calorimeters designed for measuring the heating power of ferrofluids. These methods range from simple models based on a single heat loss parameter to more advanced multi-parameter differential equations that account for complex heat loss mechanisms. One of the most widely used models for non-adiabatic conditions is the corrected-slope method [16], which represents heat loss with a single linear parameter. More sophisticated models introduce multiple thermal parameters to more accurately describe the thermal properties of the entire calorimetric system and simultaneously model various heat loss mechanisms, including dissipation effects due to radiative losses [17; 18]. Another approach to modeling non-adiabatic calorimeters involves complex and time-consuming numerical simulations using the finite element method (FEM), which allows for a more detailed analysis of thermal behavior. Although computationally demanding, this method enables a more precise assessment of heat dissipation. Researchers have also developed numerical models of nanoparticle heating [19; 20] using various experimental setups, such as inside a glass test tube [21] or within small animals [21]. Despite these advancements, the vast majority of studies evaluate their models primarily based on how well the simulated curves fit the experimental data, without explicitly assessing the measurement accuracy of their calibrated systems or comparing their models with others available in the literature. The non-adiabatic heat flow analysis, which takes place in the calorimeter, may be simplified if the thermal properties of the sample and its surroundings are represented by the lumped elements of the thermoelectric circuit. All the parameter values the model represents must be found via estimation or the calibration process.