Previous studies have indicated that a sad mood and sleep deprivation increase mind wandering, but it is unclear whether these associations reflect reduced effort in concentrating on the task at hand or diminished cognitive control. In an internet-based experiment, participants completed a sleep disturbance questionnaire followed by a complex span task and a 2-back task with thought-sampling probes. Subsequently, participants underwent a positive, neutral, or negative mood induction prior to repeating the 2-back. The results (N = 504) replicated the finding of increased task-unrelated thoughts following sad mood induction, B = 0.56 (SE = 0.14), p < 0.01, d = 0.31. Unguided thoughts were increased following sad mood induction, B = 0.31 (0.13), p = 0.02, but working memory did not significantly moderate this association (p = 0.31). People reported a lower degree of trying to concentrate on the 2-back after the sad mood induction, B = −0.07 (0.04), p = 0.04, but actual performance was not affected (p = 0.46). Sleep disturbances showed small associations with task-unrelated, B = 0.23 (0.08), p < 0.01, and unguided thoughts, B = 0.32 (0.08), p < 0.01. This study strengthens the evidence that a sad mood and poor sleep relate to mind wandering.