Automatically predicting the emotions of user-generated videos (UGVs) receives increasing interest recently. However, existing methods mainly focus on a few key visual frames, which may limit their capacity to encode the context that depicts the intended emotions. To tackle that, in this paper, we propose a cross-modal temporal erasing network that locates not only keyframes but also context and audio-related information in a weakly-supervised manner. In specific, we first leverage the intra- and inter-modal relationship among different segments to accurately select keyframes. Then, we iteratively erase keyframes to encourage the model to concentrate on the contexts that include complementary information. Extensive experiments on three challenging video emotion benchmarks demonstrate that our method performs favorably against state-of-the-art approaches. The code is released on https://github.com/nku-zhichengzhang/WECL.