Brian, I'm not sure brumation will "solve" your clutch issues but if male sperm fertility is an issue, the cooling should help. While brumation is an acceptable practice to ready many snakes for the upcoming breeding season many corns and other snakes breed fine with no cooling period. That said, I think if you want to brumate your snakes, here's what has worked for me.
1. Maintain normal heating but stop feeding the snakes. Let them fully digest their last meal for a period of 2-3 weeks. I will also soak the snakes in tepid water for 20 minutes. I notice this helps some of my snakes fully eliminate anything in their digestive tract. Anything left in the snakes can cause infection and rot with the ensuing cooler temperatures.
2. After approx 3 weeks since their last meal, turn off the heat to their tanks. At this time you can either leave them in their original tanks or move them to ventilated plastic storage tubs. The only requirement they need during brumation is water. Check this weekly but try and keep the disturbances to a minimum. I have moved them to tubs and left in their original tanks with similar success. I used aspen bedding and a hide along with the water dish.
3. I feel you should also make the room as dark as possible as well. I feel snakes not only benefit from a cool down period but a decrease in light as well. This afterall, mimics the reduced light in the winter months. Keep temps between 55 and 65 degrees F. I live in Ohio and my basement serves as a perfect brumation area.
4. I typically feed my snakes their last meal in October, start cooling down in November and start warming them back up the end of February.
5. In Spring, warm the tanks to their normal range and let the snakes "warm-up" for a period of 5-7 days. This will get their systems ready for digestion. After a week of getting warmed up, feed a smaller-than-normal meal. Wait 5 days and if you have no trouble with regurgitation feed a normal sized meal and then resume your weekly feeding schedule. Feed the females heavy to build up reserves for egg laying. Your males may refuse food for several weeks at the height of breeding season. This is considered normal for many males. They would rather breed than eat.
6. Make certain your snakes are in excellent health prior to cooling down.
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Ken Roshak
BlackSwampSerpents@toast.net