The way we evaluate an experience can be influenced by contextual factors that are unrelated to the experience at hand. A prominent factor that has been shown to infuse into the evaluation processes is incidental affect. Prior research has examined the role of such incidental affect by either focusing on its valence or its arousal, while neglecting the interplay of these two components in the affect infusion process. Based on the affect-integration-motivation (AIM) framework from affective neuroscience, our research proposes a novel arousal transport hypothesis (ATH) that describes how valence and arousal of an affective state jointly influence the evaluation of experiences. We test the ATH in a set of multimethod studies combining functional magnetic resonance imaging (fMRI), skin conductance recording, automated facial affect recording, and behavioral approaches across a range of sensory modalities including auditory, gustatory, and visual. We find that positive incidental affect, induced by viewing affect-laden pictures (vs. neutral pictures) or winning (vs. not winning) monetary rewards, enhances how much an experience (i.e., listening to music, consuming wines, or looking at images) is enjoyed. Tracking moment-based changes of affective states at the neurophysiological level, we demonstrate that valence mediates reported enjoyment and that arousal is necessary to implement and moderate these mediating effects. We rule out alternative explanations for these mediation patterns such as the excitation transfer account and the attention narrowing account. Finally, we discuss how the ATH framework provides a new perspective to explain divergent decision outcomes caused by discrete emotions and its implications for effort-based decision-making.