Keyword Spotting (KWS) models on embedded devices should adapt fast to new user-defined words without forgetting previous ones. Embedded devices have limited storage and computational resources, thus, they cannot save samples or update large models. We consider the setup of embedded online continual learning (EOCL), where KWS models with frozen backbone are trained to incrementally recognize new words from a non-repeated stream of samples, seen one at a time. To this end, we propose Temporal Aware Pooling (TAP) which constructs an enriched feature space computing high-order moments of speech features extracted by a pre-trained backbone. Our method, TAP-SLDA, updates a Gaussian model for each class on the enriched feature space to effectively use audio representations. In experimental analyses, TAP-SLDA outperforms competitors on several setups, backbones, and baselines, bringing a relative average gain of 11.3% on the GSC dataset.