Following the neurophenomenological approach, we propose a model of emotional emergence that identifies the experimental structures of time (i.e., anticipation, crisis, and aftermath) involved in emotional experience and their plausible components in terms of cognition, physiology, and neuroscience. We argue that surprise, as a lived experience, and its physiological correlates of the startle reflex and cardiac defense are the core of the dynamic, and that the heart system sets temporally in motion the dynamic of emotional emergence. Finally, in reference to Craig's model of emotion, we propose an integrative model of the temporal dynamic of emotional emergence that allows emotions to be distinguished depending on each temporal phase and that involves the following three systems: the brain (3rd person), the consciousness (1st person), and the doubled-sided (subjective/objective) continuum of the body-heart context, with the heart as the focus within the body during emotion. This model provides the framework for future developments in 1st- and 3rd-person approaches for an integrative understanding of the science of emotion, including the fields of psychophysiology and psychopathology.