With the deepening of industrial technology, the monitoring of the thermodynamic state of complex equipment systems has become a key to ensuring production continuity and safety. The thermodynamic state not only reflects the immediate working performance of the equipment but is also decisive in preventing overheating failures. The application of real-time remote monitoring technology provides a new solution for equipment health management, significantly reducing unexpected downtime, preventing failures, thus improving production efficiency and equipment lifespan. However, existing research still shows limitations in real-time data analysis, diversity of equipment adaptability, and accurate fault prediction. This paper proposes three innovative algorithms for the real-time remote monitoring of the thermodynamic state of complex equipment systems, and a method for mining overheating early warning information. The first algorithm, based on reconstruction error, is suitable for equipment with a large amount of normal operation data, using machine learning technology to accurately simulate the normal state to identify anomalies. The second single-class monitoring algorithm, suitable for situations with only normal operating data, can effectively detect deviations from the normal thermodynamic parameters. The third algorithm, based on statistical quantities, uses the statistical characteristics of equipment operation data for fault warning. In addition, the paper explores the application of the Bucket Sorting Fpgrowth algorithm in the mining of overheating early warning information of the thermodynamic state, analyzing potential fault modes and association rules through efficient data mining technology. These methods not only enhance the applicability and predictive accuracy of monitoring algorithms but also provide valuable decision support for equipment managers.