In this work we address the problem of short-term load forecasting. We propose a generalization of the linear state-space model where the evolution of the state and the observation matrices is unknown. The proposed blind Kalman filter algorithm proceeds via alternating the estimation of these unknown matrices and the inference of the state, within the framework of expectation-maximization. A mini-batch processing strategy is introduced to allow on-the-fly forecasting. The experimental results show that the proposed method outperforms the state-of-the-art techniques by a considerable margin, both on load profile estimation and peak load forecast problems.