Accurate electric load forecasting is a critical factor in ensuring the stable operation of the power grid. However, extreme weather conditions can cause significant fluctuations in electric load, increasing the complexity and uncertainty of forecasting. To address this challenge, this study proposes a short-term electric load forecasting method based on the Mamba-Transformer model under extreme weather. Initially, Mamba utilizes a state space model (SSM) to learn features and temporal relationships from the input load sequence, capturing global patterns within coarse-grained long-term time series. Next, the attention mechanism of the Transformer is employed to identify local details and short-term fluctuations, focusing on capturing local variations within fine-grained short-term time series. To validate its superiority, experiments were conducted using electricity load datasets from Belgium under extremely low temperatures and Australia under extremely high temperatures. The experimental results demonstrate that the proposed method outperforms other advanced forecasting methods, exhibiting superior accuracy and stability.