Not exactly a cycle, there was a final period at the end of last ice age called the Younger Dryas (https://en.wikipedia.org/wiki/Younger_Dryas). This stage brought disastrous low temperatures, lower than at the peak of the whole ice age. Probably it was caused by multiple asteroid/comet impacts on the ice sheet, especially in the North America. The evidence was found in many places by geologists in US who exposed “black layers” in the ground layers dated at around 11 000 bc (https://www.pnas.org/doi/10.1073/pnas.0800560105) or alternatively it was caused by volcanic eruption of the Laacher See volcano in present Germany. In both cases – at the end of ice age there was a global catastrophy causing floods and temperature decrease. Hence the myths about global flood in the Bible/Gilgamesh/Atra-Hasis/Matsa-Purana records 🙂

It’s a cycle that the earth goes through regularly. It’s caused by a fluctuating sun and is probably the main cause of any cooling we’re experiencing today.