In the field of temperature safety monitoring, it is important to quickly locate the position of temperature anomalies and start to alarm. The multimode fiber (MMF) has a certain temperature hysteresis effect when detecting the surrounding temperature along the sensing fiber, it deteriorates the warning-time of Raman distributed temperature sensor (R-DTS). This paper proposed and experimentally demonstrated an R-DTS with heat transfer functional model to perceive the surrounding temperature in advance. The temperature hysteresis effect of MMF cable in different temperature conditions are studied experimentally. The experimental results show that the temperature change rate of MMF and the surrounding temperature difference maintains a linear relationship after fitting. And this fitting relationship is used to perceive the surrounding temperature anomalies along the MMF for R-DTS system. The experimental results indicate that the warning-time of R-DTS can optimize from 23.4 s to 1.3 s at the temperature condition with 60 °C. It proves that this analytical model of the heat transfer function model can quickly perceive the environment temperature anomalies to avoid the temperature hysteresis effect of MMF at the difference temperature conditions. The research content can be applied in the temperature safety monitoring with high requirements for early-warning time, such as fire monitoring, power cable safety monitoring, and gas pipeline leakage detection.