Active learning is an iterative labeling process that is used to obtain a small labeled subset, despite the absence of labeled data, thereby enabling to train a model for supervised tasks such as text classification. While active learning has made considerable progress in recent years due to improvements provided by pre-trained language models, there is untapped potential in the often neglected unlabeled portion of the data, although it is available in considerably larger quantities than the usually small set of labeled data. Here we investigate how self-training, a semi-supervised approach where a model is used to obtain pseudo-labels from the unlabeled data, can be used to improve the efficiency of active learning for text classification. Starting with an extensive reproduction of four previous self-training approaches, some of which are evaluated for the first time in the context of active learning or natural language processing, we devise HAST, a new and effective self-training strategy, which is evaluated on four text classification benchmarks, on which it outperforms the reproduced self-training approaches and reaches classification results comparable to previous experiments for three out of four datasets, using only 25% of the data.