In twenty-plus years of breeding gila monsters I always cooled them to roughly 55 F for three or four months to get viable egg clutches. However, when I kept them, I found this not to be the case with beaded lizards as I had fertile clutches of eggs three years in a row with no more than a nightly drop in the ambient room temperature from 81 F to 76 F. (I would have dropped it lower but I had tree monitor enclosures in the same room) This leads me to conclude that brumation/hibernation is NOT neccesary for the succesful reproduction of nominate beadeds.
If you do choose to brumate make sure your waterdish is SPILLPROOF and use a DRY substrate. (I used beta-chip or aspen-chip with a piece of 5" sono-tube to hide in for H.s.suspectum ) The slow evaporation of the water dish (which should be checked at least monthly) will provide ambient humidity when enclosed in a large bin.
Just my experiences and observations.
Dave