## 1 Introduction  
Since the 1980s, phototherapy and hyperthermia treatment in cancer therapy have attracted considerable attention due to their unique therapeutic effects [1; 2; 3; 4]. Compared to chemotherapy and radiotherapy, these techniques have minimal side effects, further contributing to maintaining a high level of research interest. These treatments crucially require continuous monitoring of temperature distribution to avoid damaging normal cells, as deviations in temperature cause irreversible harm during treatment. Therefore, phototherapy and hyperthermia treatment should be accompanied by a real-time temperature measurement technique. Inorganic luminescence thermometers have emerged as a solution, offering real-time, rapid response and high sensitivity remote temperature measurements. Luminescence thermometers within the biological transparent window (BTW) are particularly advantageous for temperature detection from deep tissue. The BTW can be separated into three wavelength regions, 650-950 nm (1 st), 1000-1350 nm (2 nd), and 1550-1870 nm (3 rd), which are summarized based on the spontaneous fluorescence, absorption effects from biological tissues, and the inverse fourth power of the Rayleigh scattering effect concerning the wavelength [5; 6]. In the past two decades, for the research of luminescence thermometers, a widely employed strategy is the combination of the ratiometric method and Boltzmann distribution, which relies on the luminescence intensity ratio from two thermally coupled energy levels of the luminescence center ion in inorganic host material. The population of these two energy levels is determined by the Boltzmann distribution [7; 8; 9; 10]. The most widely used Boltzmann thermometer is based on the thermally coupled energy levels of Er\({}^{3+}\)\({}^{4}\)S\({}_{3/2}\)/\({}^{2}\)H\({}_{11/2}\). One of the interesting applications of it has been its use in measuring the local temperature gradients during catalytic reactions [11]. Furthermore, other luminescence ions have been investigated from the luminescence wavelength and temperature rae viewpoint. Boltzmann thermometers based on Ho\({}^{3+}\): \({}^{5}\)F\({}_{4}\)/\({}^{5}\)F\({}_{5}\)[12; 13], and Eu\({}^{3+}\): \({}^{5}\)D\({}_{0}\)/\({}^{5}\)D\({}_{1}\)[14] have been gradually developed for high-temperature detection because of the high energy difference between these pairs of thermally coupled levels, exceeding 1500 cm\({}^{-1}\). However, these Boltzmann thermometers work within the visible range; when used for deep tissue temperature measurement, they are affected by Rayleigh scattering, spontaneous fluorescence from biological tissues, and absorption effects, leading to reduced temperature measurement accuracy. NIR Boltzmann thermometers have become the hotspot for deep tissue temperature measurement in recent years. Nd\({}^{3+}\) ion is often seen as an ideal NIR luminescence center for its excitation and emission within the BTW. However, the less-than-perfect energy differences (\(\Delta E\)) between two pairs of thermally coupled energy levels of Nd\({}^{3+}\) bring about a technical bottleneck for temperature measurement applications. Nd\({}^{3+}\): \({}^{4}\)F\({}_{3/2}\)/\({}^{4}\)F\({}_{5/2}\) with a \(\Delta E\) of up to 1000 cm\({}^{-1}\) results in a deviation from the theoretical LIR value after the temperature drops below 300 K [15]. On the other hand, the relative sensitivity of temperature measurement based on the thermally coupled Stark sublevels of Nd\({}^{3+}\): \({}^{4}\)F\({}_{3/2}\) is low due to a \(\Delta E\) value as low as 100 cm\({}^{-1}\) (not exceeding 0.7% K\({}^{-1}\)) [16; 17; 18]. Therefore, one approach to overcome this technical bottleneck is to find a NIR luminescence center with a moderately suitable \(\Delta E\) value. Yb\({}^{3+}\)-doped GAGG is more advantageous for luminescence temperature measurement applications.