This work, termed MH-LVC, presents a multi-hypothesis temporal prediction scheme that employs long- and short-term reference frames in a conditional residual video coding framework. Recent temporal context mining approaches to conditional video coding offer superior coding performance. However, the need to store and access a large amount of implicit contextual information extracted from past decoded frames in decoding a video frame poses a challenge due to excessive memory access. Our MH-LVC overcomes this issue by storing multiple long- and short-term reference frames but limiting the number of reference frames used at a time for temporal prediction to two. Our decoded frame buffer management allows the encoder to flexibly utilize the long-term key frames to mitigate temporal cascading errors and the short-term reference frames to minimize prediction errors. Moreover, our buffering scheme enables the temporal prediction structure to be adapted to individual input videos. While this flexibility is common in traditional video codecs, it has not been fully explored for learned video codecs. Extensive experiments show that the proposed method outperforms VTM-17.0 under the low-delay B configuration in terms of PSNR-RGB across commonly used test datasets, and performs comparably to the state-of-the-art learned codecs (e.g.~DCVC-FM) while requiring less decoded frame buffer and similar decoding time.