Thermal state monitoring of high-voltage electrical equipment is crucial for ensuring the safety and stability of power grids. Traditional contact-based temperature measurement methods are susceptible to interference in high-voltage environments, while infrared thermal imaging suffers from limitations such as low spatial resolution, high cost, and strong dependence on surface emissivity. Recently, visible-light image-based temperature measurement techniques have gained attention due to their high spatial resolution, low hardware cost, and easy integration with existing surveillance systems. However, existing methods often rely on large annotated datasets and exhibit limited generalization in the presence of scarce high-temperature fault samples. This paper proposes a non-contact temperature estimation and fault identification method based on the intensity component in the HSI color space. By establishing a power-law relationship between image intensity and temperature, the model effectively extrapolates to high-temperature conditions using readily available low-temperature images. Furthermore, a fault discrimination strategy based on a statistical confidence mechanism is introduced to handle limited low-temperature sample ranges, enabling reliable anomaly detection via a critical intensity threshold. Experimental results on copper, aluminum, and iron demonstrate that the model achieves strong extrapolation performance when the low-temperature sample range exceeds approximately 45 °C, and remains effective for fault monitoring even within narrower ranges by adjusting the confidence level.