We present a method for autogenerating a large domain-specific question-answering (QA) dataset from a thermoelectric materials database. We show that a small language model, BERT, once fine-tuned on this automatically generated dataset of 99,757 QA pairs about thermoelectric materials, affords better performance in the field of thermoelectric materials compared to a BERT model fine-tuned on the generic English-language QA data set, SQuAD-v2. We further show that mixing the two data sets (ours and SQuAD-v2), which have significantly different syntactic and semantic scopes, allows the BERT model to achieve even better performance. The best-performing BERT model fine-tuned on the mixed data set outperforms the models fine-tuned on the other two data sets by scoring an exact match of 67.93% and an 1 score of 72.29% when evaluated on our test data set. This has important implications as it demonstrates the ability to realize high-performing small language models, with modest computational resources, empowered by domain-specific materials data sets which can be generated according to our method.