Decoder-only transformers are the backbone of the popular generative pre-trained transformer (GPT) series of large language models. In this work, we employ this framework to the analysis of clinical heart time-series data, to create two pre-trained general purpose cardiac models, termed PPG-PT and ECG-PT. We place a special emphasis on making both such pre-trained models fully interpretable. This is achieved firstly through aggregate attention maps which show that, in order to make predictions, the model focuses on similar points in previous cardiac cycles and gradually broadens its attention in deeper layers. Next, we show that tokens with the same value, which occur at different distinct points in the electrocardiography (ECG) and photoplethysmography (PPG) cycle, form separate clusters in high dimensional space. The clusters form according to phase, as the tokens propagate through the transformer blocks. Finally, we highlight that individual attention heads respond to specific physiologically relevent features, such as the dicrotic notch in PPG and the P-wave in ECG. It is also demonstrated that these pre-trained models are straightforward to fine-tune for tasks such as classification of atrial fibrillation (AF), and beat detection in photoplethysmography. For the example of AF, the fine-tuning took 11 minutes of computer time, and achieved the respective leave-one-subject-out AUCs of 0.99 and 0.93 for ECG and PPG within the MIMIC Perform AF dataset. In addition, the fine-tuned beat detector achieved a state-of-the-art F1 score of 98%, as well as uniquely providing a beat confidence level which acts as a signal quality estimator. Importantly, the fine-tuned models for AF screening are also fully explainable, with attention shifting to regions in the context that are strongly indicative of atrial fibrillation.