You're incorrect about your assumptions. If you click the link in the parent post, you'll see that temperatures swung as much as 8C during the ice age. These events are called Dansgaard-Oeschger events (https://en.wikipedia.org/wiki/Dansgaard%E2%80%93Oeschger_eve...) The warming would happen rapidly (within 3 decades), followed by a stepped down cooling period (often lasting hundreds of years). This happened repeatedly during the most recent glacial.
And then more recently, after the last glacial period had ended, you had incidents like the Younger Dryas, for example, where temps plunged to near ice age levels (up to 6C drop in a few decades) and then rapidly warmed all of a sudden. If you read https://en.wikipedia.org/wiki/Younger_Dryas) some are suggesting that a warming episode at the end of the Younger Dryas occurred in as little as a few years and warmed global temps by 7C.
And then more recently, after the last glacial period had ended, you had incidents like the Younger Dryas, for example, where temps plunged to near ice age levels (up to 6C drop in a few decades) and then rapidly warmed all of a sudden. If you read https://en.wikipedia.org/wiki/Younger_Dryas) some are suggesting that a warming episode at the end of the Younger Dryas occurred in as little as a few years and warmed global temps by 7C.
Note, that by the end of the Younger Dryas, the Arctic was as much as 7C hotter than it is today (https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019...).
There's thousands of papers on the Little Ice Age. It certainly shows up all over the world in the fossil record. https://www.sciencedirect.com/search/advanced?qs=little%20ic...