Recent works on source-free domain adaptation (SFDA) for time series reveal the effectiveness of learning domain-invariant temporal dynamics on improving the cross-domain performance of the model. However, existing SFDA methods for time series mainly focus on modeling the original sequence, lacking the utilization of the multi-scale properties of time series. This may result in insufficient extraction of domain-invariant temporal patterns. Furthermore, previous multi-scale analysis methods typically ignore important frequency domain information during multi-scale division, leading to the limited ability for multi-scale time series modeling. To this end, we propose LEMON, a novel SFDA method for time series with wavelet-based multi-scale temporal imputation. It utilizes the discrete wavelet transform to decompose a time series into multiple scales, each with a distinct time-frequency resolution and specific frequency range, enabling full-spectrum utilization. To effectively transfer multi-scale temporal dynamics from the source domain to the target domain, we introduce a multi-scale temporal imputation module which assigns a deep neural network to perform the temporal imputation task on the sequence at each scale, learning scale-specific domain-invariant information. We further design an energy-based multi-scale weighting strategy, which adaptively integrates information from multiple scales based on the frequency distribution of the input data to improve the transfer performance of the model. Extensive experiments on three real-world time series datasets demonstrate that LEMON significantly outperforms the state-of-the-art methods, achieving an average improvement of 4.45% in accuracy and 6.29% in MF1-score.