In automated driving, drivers may sleep during rides, making it important to study napping preferences and wake-up scenarios for human-centered system design. We conducted an online study with 280 participants, balanced by age and gender, examining how often, when, and how long individuals would nap if given the opportunity. The study also explored preferred wake-up methods when the vehicle nears the end of its operational design domain. Using a mixed 2 × 2 design, participants were assigned to one of two travel purposes (“commuting” vs. “holiday trip”) and two minimal risk conditions (rest area vs. hard shoulder). The results showed that 40% intended to sleep during automated driving, highlighting a strong interest in in-car sleeping. Wake-up preferences varied by travel purpose and minimal risk condition, with many favoring awakening before the drive ended. Participants also anticipated sleep inertia and desired post-wake-up support. The findings allow suggestions for designing wake-up concepts that mitigate sleep inertia.