Research has shown that curiosity plays a crucial role in human performance and well-being. Based on multi-dimensional models of curiosity, we examined potential underlying mechanisms for this relationship. Extending prior research, we expected state and trait variants of curiosity to predict more challenge and less threat appraisals for novel tasks (i.e., joyous exploration dimension), stronger dissatisfaction when denied opportunities to do something interesting (i.e., deprivation sensitivity dimension), and persist longer under stress states (i.e., stress tolerance). We asked 123 participants to prepare and deliver a speech titled "Why are you a good friend?" After preparation, participants were informed that they were randomly selected not to perform the task. Throughout the experiment, we recorded heart rate reactivity as a physiological indicator of task engagement. We found that individuals curious about the upcoming task felt more challenged, less threatened, and presented longer physiological engagement than less curious individuals. Curious individuals expressed more disappointment about the missed opportunity to deliver the speech. In summary, this study revealed theoretically derived mechanisms that partially account for associations between curiosity and positive life outcomes while also indicating adverse effects.