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In this paper, we propose new evaluation method for thermal conductivity measurement of single carbon nanotube (CNT) in liquid with hydrogel sensor containing quantum dot (Q-dot). Measurement of thermal property of single CNT in liquid is quite difficult because escape of the heat from measurement device. Therefore, novel evaluation method using the hydrogel sensors for both thermal input and temperature sensing was proposed. We can measure the local temperature by fluorescence intensity from the sensors. This sensor is also used for thermal input by absorption of near infrared (IR) laser to Q-dots. In our proposed model, two gel-sensors are adhered to both edges of the CNT. Heat is input to CNT through the gel-sensor. Heat transferred through the CNT is detected using the other sensor by measuring the temperature at the edge of the CNT. Sensitivity of the sensor is -1.1%/K and accuracy is ±0.5 K. The error of heat input is within 5%. Thermal conductivity was calculated from the proposed method. The estimated error of the thermal conductivity in our model is about 20%. We demonstrated the preliminary evaluation of the thermal conductivity of single CNT using the gel-sensors in liquid.