## 1 Introduction  
Atmospheric pressure helium dielectric-barrier discharges (APHeDBDs) have been developed intensively in different fields including surface treatments [1; 2; 3] and plasma medicine [4; 5; 6] due to the efficient generation of reactive species and stable operating conditions. Typically, APHeDBDs are driven by kHz power sources since they are simple and can be scaled up for applications easily. Therefore, APHeDBDs driven by kHz power sources can be considered as one of the important plasma sources for the aforementioned applications. It is common to consider gas temperature as one of critical discharge parameters since gas temperature influences rate constants of chemical reactions and densities of background gases, determining the discharge chemistry. Gas temperature is also the key parameter affecting transport properties (i.e., diffusivities), which may lead to different transport behavior. Moreover, it is critical to control the gas temperature for applications with materials that are sensitive to heating load. Hence, it is essential to control the gas temperature of APHeDBDs. The gas temperature of a helium discharge is typically obtained by determining the rotational temperature from the emission spectrum of N\({}_{2}\) second positive system (SPS, N\({}_{2}\)(C\({}^{3}\Pi_{u}\))\(\rightarrow\)N\({}_{2}\)(\(B^{3}\Pi_{g}\))) measured via an optical emission spectrometer (OES) with the addition of low N\({}_{2}\) concentration (e.g., \(\sim\)0.1%) [7; 8; 9]. The helium discharge can be sustained at a wide range of gas temperatures ranging from room temperature (e.g., 300 K) to a few hundred degrees Kelvin [9; 10; 11], depending on the operating conditions. Therefore, it is necessary to control and determine the gas temperature properly. From the application perspective, it is important to realize the heating mechanisms for optimizing an appropriate reactor and controlling at proper operating conditions. However, the measurements of the rotational temperatures at various operating conditions provide no further information on heating mechanisms of complex discharge behavior. Fortunately, numerical simulations provide another alternative to reveal details of discharge dynamics. APHeDBDs have been studied numerically for years due to their importance for applications [12; 13; 14; 15; 16]. In general, the simulated results were obtained efficiently with the one-dimensional (1D) plasma fluid model (PFM) by solving the species continuity equations, the Poisson equation, and the electron energy density equation to model the spatial and temporal changes of species densities, electric field, and electron temperature, respectively, for capturing the complex discharge dynamics. Although APHeDBDs can be operated as uniform glow-like discharges that are modeled appropriately by the 1D PFM, it was identified that APHeDBDs can also be operated as the patterned non-uniform discharges [17; 18]. Hence, it is important to examine the discharge uniformity before employing the 1D PFM to model the APHeDBDs. Moreover, it was reported that a small amount of N\({}_{2}\) (e.g., a few ppm) may play the dominant role in APHeDBDs due to Penning ionization and associative processes among excited helium species, helium ions, and N\({}_{2}\) molecules [12; 15; 16]. Therefore, it is essential to model APHeDBDs with the proper concentration of N\({}_{2}\) added for temperature measurements. The mechanisms of gas heating in atmospheric pressure helium discharges have been studied for years [9; 19; 20; 21; 22]. The gas heating effects of atmospheric pressure helium microplasmas sustained by the dc power sources were investigated with either the 1D or 2D PFM in conjunction with the 2D gas flow model (GFM) considering ion Joule heating as the heating source for modeling the gas temperature in the discharge [9; 19]. It was identified that most (\(\sim\)87%) of the total input power goes to gas heating and the gas temperature increases to \(\sim\)650 K due to the ion Joule heating. [PERSON] et al.