The paper presents a method for spoken term detection based on the Transformer architecture. We propose the encoder-encoder architecture employing two BERT-like encoders with additional modifications, including convolutional and upsampling layers, attention masking, and shared parameters. The encoders project a recognized hypothesis and a searched term into a shared embedding space, where the score of the putative hit is computed using the calibrated dot product. In the experiments, we used the Wav2Vec 2.0 speech recognizer, and the proposed system outperformed a baseline method based on deep LSTMs on the English and Czech STD datasets based on USC Shoah Foundation Visual History Archive (MALACH).