## 1 Introduction  
The accurate prediction of aerodynamic heating is important in the thermal and structural design of hypersonic flight vehicles, and its prediction remains a difficult problem in modern computational fluid dynamics. Experimental measurements still play an indispensable role in addressing this problem. Although much progress has been made in improving the accuracy of heat transfer measurements in recent decades, a difference of \(\pm\)10% between the experimental and theoretical results is often observed, e.g., for a sharp cone standard model [1]; the difference might be even larger at certain local regions of more complex model shapes [2]. In addition, the measuring accuracy also depends on the test conditions and the sensor type. Thus, it remains necessary to extensively develop new heat flux sensors and investigate the factors influencing the heat transfer measurements before further progress can be made. Due to the flows ranging from 2.5 to 45 MJ/kg, which correspond to velocities from 2 to 10 km/s, respectively [3; 4]. In such facilities, where the effective test time is on the order of milliseconds, the heat flux rate is derived from the transient temperature monitored at selected points on the model with fast response testing technology. Generally, the techniques can be divided into two categories; the first is based on heat flux sensors, such as resistance thermometers [5; 6; 7; 8], thermocouples [9; 10; 11; 12; 13], and calorimeters [14; 15; 16; 17], and the second is based on non-intrusive techniques such as temperature-sensitive paint [18; 19] and thermography [20; 21]. However, each technique has its own benefits and challenges. For example, non-intrusive optical measurements are a candidate for obtaining global temperature distribution measurements and have temporal/spatial advantages. However, the calibration procedures are very cumbersome, and the accuracy can be seriously affected by impurities of the flow field and vibration of the model. Overall, this technique remains technologically immature. Because of these optical drawbacks, point heat flux sensors, which are typically cylindrical in shape, are primarily used for heat transfer measurements [22]. These sensors must have a sufficiently fast response to obtain enough data and must withstand from thermal damage or rapid erosion due to fragments of the metallic and plastic diaphragms that hit the models at high speeds. Among point heat flux sensors, thin-film resistance gauges have very short rise times and high electrical output per degree rise in temperature. However, they are limited to low-enthalpy flows and are prone to thermal damage or rapid erosion under high-enthalpy flows. The lifetime of each gauge is limited to one or two shots [23]. Thermocouples and calorimeters are relatively robust gauges. However, the junction of a thermocouple is formed either by mechanical interference or abrasion, which requires re-abrading or re-machining between shots due to damage from the flow. There are also uncertainties associated with the junction structures [24]. Moreover, the sensitivity of a thermocouple is relatively low at tens of microvolts per degree (about 61 \(\upmu\)v/K for a type-E thermocouple at 300 K [25]). Besides, both thin films and thermocouples can suffer from interference from ionized flows due to exposed metallic elements [26], and insulating coatings to prevent this are typically fragile or affect the performance. In contrast, in a calorimeter-style gauge, the temperature sensing element can be shielded from direct contact with the erosive flows. This sensor also has the advantages of straightforward production and low cost and is suitable for fabrication or modification according to various requirements in the laboratory. Calorimeter gauges are based on calculating the instantaneous heat transfer rate by measuring the time rate of change of the thermal energy in a metal element.