Single-stream structures are prevalent in RGB-T saliency detection due to their efficiency and lightweight nature. However, existing multi-modal single-stream methods suffer from limited detection performance, primarily due to inadequate exploitation of thermal modality's strengths. To address this, we propose a novel single-stream network called Thermal-induced Modality-interaction Multi-stage Attention Network (TMMANet). Our approach leverages thermal-induced attention mechanisms in both the encoder and decoder stages to effectively integrate RGB and thermal modalities. In the encoder, a Thermal-induced Modality-interaction Self-Attention mechanism is introduced to extract powerful cross-modal features. In the decoder, a Thermal-induced Modality-interaction Dual-Branch Attention mechanism is designed to generate accurate saliency predictions by constructing modality-aware integration of foreground and background branches. Extensive experiments demonstrate that TMMANet outperforms most state-of-the-art RGB-T, RGB and RGB-D methods under various evaluation metrics, this highlights its effectiveness in enhancing RGB-T saliency detection performance. The related data of our TMMANet are released at https://github.com/SUTPangYu/TMMANet.