## 3 Theoretical Analysis and Simulation Model of Temperature Error
### Joule Heat  
The Pt thin film sensor will generate Joule heat when it works, and the magnitude of Joule heat is related to the applied voltage and the Pt thin film resistance. Increasing the resistance value of the Pt thin film is necessary to enhance the sensor's sensitivity. When the temperature changes, the greater the resistance change value is, and the greater the current change value is, the more sensitive the sensor is. Equation (5) shows the relationship between the current change and resistance value:  
\[\Delta I=\frac{U}{\Delta R}=\frac{U}{R_{0}[1+\alpha(t-t_{0})]0} \tag{5}\]  
where \(\Delta I\) is the current variation value, and \(\Delta R\) is the voltage variation value. However, the larger the resistance value, the larger the Pt thin film volume, leading to a larger sensor volume and Joule heat. Therefore, considering comprehensively, the resistance value of the Pt thin film was set to about 100 \(\Omega\) (0 \({}^{\circ}\)C). The Joule heat of the sensor was also analyzed to obtain the temperature sensor's measurement error and response time under the co-effect of rated voltage and heat dissipation. To analyze the influence of different mechanical structures on the performance of the temperature sensor, we designed six insulators, as Figure 3 shows. The main difference between these six insulators was the size of the contact area between the platinum film and the insulator, which was used to study the effect of the contact area size on sensor performance. The contact area between the two increases sequentially from Insulator 1 to Insulator 5. In addition, Insulator 6 was designed for comparison with Insulator 5 to show the performance of the thermal insulation tank. During the Joule thermal simulation of the temperature sensor, a voltage of 0.04 V was applied to both ends of the Pt thin film to study the influence of environment temperature on Joule heat. We set the ambient temperature at 233.15 K, the absolute pressure at 50 Pa, and the wind speed at 100 m/s. The initial temperature of the sensor was set at 228.15 K and 238.15 K, respectively. We compared the response time and Joule heat of six types of sensors to select the best insulator. The response time of the temperature sensor is represented by \(\tau\), and \(\tau\) refers to the time required for the output change of the temperature sensor to reach 63.2% of the difference between its initial final value [39]. The Joule heat of the sensor was analyzed to obtain the temperature variation and response time of the temperature sensor under the combined effect of rated voltage and heat dissipation. The electrical load of the Pt thin film was determined before probing, the Joule heat generated by the current during probing was steady, and the air pressure further influenced the temperature value of the Pt thin film by affecting the heat transfer coefficient. The equations for heat dissipation and Joule heat of a Pt thin film are as follows:  
\[Q_{2}=A_{2}\lambda_{2}\cdot\Delta T_{2} \tag{6}\]  
\[Q_{A}=\frac{U^{2}\mathrm{t_{s}}}{R} \tag{7}\]  
where \(Q_{2}\) is the heat dissipated, \(A_{2}\) is the contact area between the Pt thin film and the air, \(\lambda_{2}\) is the heat transfer coefficient between them, \(\Delta T_{2}\) is the temperature difference between the two sides of the Pt thin film-air interface, \(Q_{A}\) is the joule heat, and \(\mathrm{t_{s}}\) is the unit time. Thus, the amount of heat gain in the Pt thin film due to Joule heat is expressed as Equation (8):  
\[Q_{a}=Q_{A}-Q_{1}-Q_{2}=\frac{U^{2}\mathrm{t_{s}}}{R}-A_{1}\lambda_{1}\cdot \Delta T_{1}-A_{2}\lambda_{2}\cdot\Delta T_{2} \tag{8}\]  
Figure 3: The six types of insulator with increasing areas from (**1**) to (**6**).