The current Milankovich Cycle ends in about 800-1200 years, by which time we'll have had about 10-11,000 years of reliably warm climate. This change should be followed immediately by a pleniglacial stage, in which students of these big climatic breaks tell us we'll go from near-full interglacial conditions, and warm temps, to full-glacial conditions in about 20 years.
Your point about CO2 and other greenhouse gases is well taken. When this interglacial ends, we'll be burning every chunk of coal in China just to put more greenhouse gases into the atmosphere.