Incidental affect has an important impact on intertemporal choice (IC). This research aimed to test how positive incidental affect influences IC and its underlying mechanisms. We assumed that positive incidental affect may have a disjunction effect on IC that includes or excludes immediate time. Moreover, we examined the role of time perception for the effect of affect on IC. In Study 1, after undergoing affect priming by video clips, participants completed the IC task using a multiple staircase paradigm. Using Hierarchical Bayesian Modeling, we estimated the discount rate parameter by distinguishing “immediate” and “non-immediate” conditions of IC. The participants’ time perception was also measured. In Study 2, apart from the choice preference of IC, we additionally investigated the differences in the participants’ attention to delay and reward attributes before decision making. The results of the two studies indicated that positive incidental affect leads to longer time perception (Study 1) and prior and more attention to the delay attribute of IC (Study 2), which leads individuals to prefer immediate options in the IC (Studies 1 and 2). Moreover, there is a disjunction effect of affect; in other words, the incidental affect did not influence IC excluding immediate time (Studies 1 and 2). This study improves our understanding of the disjunctive effect and its mechanism of inducing a positive incidental affect on IC and thus provides a new perspective on how related decision making can be improved.