Ummm... Lug-Nut. They crossed the Bering Straight during the Ice Age. Massive Glaciers covered large portions of the planet. Directly associated with that, where the lower sea levels. Sea levels that where hundreds of feet lower. Hence the Bering Straight being the Bering Land Bridge.
Sea levels do rise with global warming. All of that ice melting creates liquid water that goes into our oceans, causing the water level to rise. During global cooling, those glaciers reform, taking the water out of the oceans, lowering the levels.
Make sense now?