Automatic prediction of emotion promises to revolutionise human-computer interaction. Recent trends involve fusion of multiple data modalities - audio, visual, and physiological - to classify emotional state. However, in practice, collection of physiological data `in the wild' is currently limited to heartbeat time series of the kind generated by affordable wearable heart monitors. Furthermore, real-world applications of emotion prediction often require some measure of uncertainty over model output, in order to inform downstream decision-making. We present here an end-to-end deep learning model for classifying emotional valence from unimodal heartbeat time series. We further propose a Bayesian framework for modelling uncertainty over these valence predictions, and describe a probabilistic procedure for choosing to accept or reject model output according to the intended application. We benchmarked our framework against two established datasets and achieved peak classification accuracy of 90%. These results lay the foundation for applications of affective computing in real-world domains such as healthcare, where a high premium is placed on non-invasive collection of data, and predictive certainty.