The present study focused on involuntary thoughts about personal past events (i.e., involuntary autobiographical memories; IAMs), and involuntary thoughts about future events and plans (i.e., involuntary future thoughts; IFTs). The frequency of these involuntary thoughts is influenced by cognitive demands of ongoing activities, but the exact underlying mechanism(s) has yet to be revealed. The present study tested two possible explanations: (1) the special inhibitory mechanism switches on when one is engaged in attentionally demanding activities; (2) different levels of cognitive load interfere with cue-noticing that act as triggers for IAMs and IFTs. We report a study with pre-selected groups of participants that differed in terms of their individual level of inhibitory control capacity (high vs. low), and completed both standard and attentionally demanding versions of a laboratory vigilance task with irrelevant cue-words to trigger IAMs and IFTs, and random thought-probes to measure their frequency. To examine the level of incidental cue-noticing, participants also completed an unexpected cue-recognition task. Despite large differences between groups in inhibitory control capacity, the number of IFTs and IAMs, reported in the attentionally demanding condition, was comparable. In addition, high cognitive load reduced the number of IAMs, but not IFTs. Finally, the recognition of incidental cues encountered in the vigilance task was reduced under high cognitive load condition, indicating that poor cue-noticing may be the main underlying mechanism of cognitive load effect rather than the lack of inhibitory resources needed to suppress involuntary retrieval. This and other possible mechanisms and avenues for future research are discussed.