MW is damaging for tasks requiring sustained and divided attention, for example driving. Recent findings seem to be indicating that off-task thoughts differently disrupt drivers. The present paper delved into characteristics of off-task thoughts to assess their respective detrimental impact on driving. Twenty volunteers had to declare their MW thoughts and get intentionally involved in Problem-Solving Thoughts (PST) according to instructions. Heart rate and oculometric behavior were collected during the two sessions. Results showed that MW and PST led to a fixed gaze. MW might also led to a cognitive effort necessary to switch from task-unrelated to task-related focus. Similarities and differences between intentional and unintentional off-task thoughts were discussed in greater detail. By designing a detection algorithm, it could be possible to detect disruptive MW during risky situations while permitting the mind to wander when the driving demand is low.