Dynamic thermal management (DTM) is applied to address the thermal problem of high performance very-large-scale integrated chips. The false alarm rate (FAR) can be used to evaluate the impact of full-chip thermal field reconstruction accuracy on DTM. A low FAR relies on the accurate reconstruction of the full thermal field, especially near the temperature triggering threshold of DTM. However, little attention is currently being paid to such temperature ranges. To reduce FAR, a new full-chip thermal field reconstruction strategy is proposed. A low-dimensional linear model is used to accurately represent the thermal fields. The dictionary learning technology is exploited to train the model and the minimum weighted mean square error evaluation method is incorporated to improve the reconstruction accuracy near the temperature triggering threshold. A temperature sensor placement algorithm using the heuristic algorithm to solve the NPhard problem is also proposed. The experimental results show that the proposed strategy can reconstruct the full thermal field with a more precise accuracy near the triggering threshold and achieve the lowest FAR compared to the state of the art.