Do you have an example? Because all of the variations in recorded history, the Medieval Warm Period and Little Ice Age, were less than 0.5C. Also, both were regional and came on over centuries.

Also, the difference between the Ice Age and current interglacial was only 4C. The transition took 6000 years. We are approaching 1.5C and should hit 3C. That is the opposite of Ice Age in a century.