Breast cancer detection using thermal imaging presents a non-invasive, cost-effective screening alternative, especially suited for resource-limited environments. This paper proposes a multi-branch hybrid deep learning framework that simultaneously processes spatial thermograms and their frequency-domain Power Spectral Density (PSD) representations. A novel Shapley-value based Gated Fusion mechanism adaptively integrates complementary features extracted via a lightweight MobileNetV3Small backbone, enhancing the discriminative capability of the overall model, while maintaining computational efficiency. The model is trained and evaluated on the publicly available DMR-IR dataset of thermal breast images. Experimental results demonstrate superior diagnostic accuracy compared to prior state-of-the-art approaches, highlighting the efficacy of joint spatial-frequency feature learning for breast cancer classification. The codes for this work are available at : https://github.com/Kylian07/Shaply-based-Gated-Fusion .