An air carrier flight crew over flew their destination when they may have nodded off for a few minutes.

Narrative

Enroute to ZZZ with autopilot coupled to FMS; both crew members zoned out and/or nodded off briefly losing contact with ATC. Autopilot continued past destination airport. Regaining situational awareness contacted ATC and received vector to Hilo. Landed without further incident. Both myself and the First Officer had reported to work feeling well rested and fit to fly. Looking back; I had flown five days in a row with 8 legs day one; four on day two; eight on day three and four and this flight was the fourth of eight scheduled for day five. First Officer had flown the same with the exception of having 2 days off. 32 flight segments for me (Captain) and 28 for the First Officer in five days apparently caught up with us. Short segments 35-50 minutes long with 20 turns. And the warm sun coming through the windows may have been a factor. Closer monitoring of my own factor levels as well as my crew's level of fatigue are in order. I could have had day 2 off also; but was goaded into a junior assignment by the company. I wish I had taken the day off. Additional factor may have been the motel accommodations provided by the company. My concerns about it's quality and even more so it's security may have given me a false sense of the quality of rest I was receiving. Also when the FMS gets to the ends of the flight plan it continues to hold altitude and heading; only warning is on FMS screen in 1/4 inch letters out of one's direct view. Perhaps a link to the master caution/warning system with aural alerts would help.