Temporal action detection aims to predict the time intervals and the classes of action instances in the video. Despite the promising performance, existing two-stream models exhibit slow inference speed due to their reliance on computationally expensive optical flow. In this paper, we introduce a decomposed cross-modal distillation framework to build a strong RGB-based detector by transferring knowledge of the motion modality. Specifically, instead of direct distillation, we propose to separately learn RGB and motion representations, which are in turn combined to perform action localization. The dual-branch design and the asymmetric training objectives enable effective motion knowledge transfer while preserving RGB information intact. In addition, we introduce a local attentive fusion to better exploit the multimodal complementarity. It is designed to preserve the local discriminability of the features that is important for action localization. Extensive experiments on the benchmarks verify the effectiveness of the proposed method in enhancing RGB-based action detectors. Notably, our framework is agnostic to backbones and detection heads, bringing consistent gains across different model combinations.