Involuntary musical imagery (INMI), i.e the internal experience of a repetitive musical fragment, is one of the most ubiquitous forms of spontaneous cognition. Findings regarding the relationship between INMI and cognitive load are conflicting. In the present study, 200 participants watched and evaluated two non-dialogue, music-only film trailers. Subsequently, they either closed their eyes for 5 min (baseline), or engaged in one of three dot tasks of varying challenge and attentional demand (low, medium, and high cognitive load). Finally, they completed a novel "Mind Activity Questionnaire", which allows for indirect INMI sampling rather than direct questioning. The same questionnaire was completed 24 hours later. Overall, a significant negative linear trend was found. At baseline, 65% of people reported experiencing INMI. This rate decreased to 32.5% in the low load condition with further reductions observed in the medium and high conditions, which did not differ significantly from each other. INMI frequency and duration followed the same pattern as the induction rates. In the 24-hour follow-up, 21% of participants reported INMI experiences. This study supports the hypothesis that INMI occurrence, frequency, and duration relate to spare cognitive capacity and demonstrates an ecologically valid laboratory paradigm for covertly inducing and documenting INMI experiences.