Temporal Katz Centrality (TKC) measures node importance by aggregating time-decayed contributions from all temporal walks, emphasizing recent interactions. This enables TKC to capture the evolving influence of vertices in dynamic networks, making it a valuable tool for ranking and identifying key entities. However, computing TKC is computationally intensive due to the need to traverse all time-respecting paths. To address this challenge, we propose a temporal graph neural network-based framework. Our model utilizes a temporal graph neural network to learn node representations. To enhance efficiency, it adopts a degree-based temporal neighbor sampling strategy, selectively targeting key temporal neighbors to effectively reduce computation. Additionally, a fused long short-term memory (LSTM) module is integrated into the framework to aggregate temporal neighbor information, mimicking the accumulation of weighted temporal walk contributions. Experimental results on six real-world datasets demonstrate the effectiveness and efficiency of the proposed method.