Utilizing the specially designed low‐warming experiments of the fully coupled Community Earth System Model, we investigate the evolutions of Eurasian climate and extreme events if global mean temperature would stabilize at 1.5 °C and 2 °C above preindustrial levels or overshoot the 1.5 °C (1.5 °C OS) threshold. We find that distinctive evolutions of surface temperature (TS) and extreme events appear in different regions of Eurasia, particularly over East China and Northern Eurasia. In the course of global warming, before global mean temperature stabilizes, the two regions display similar changes of TS and extreme events. However, after global warming halts, the two regions experience distinctive evolutions of local warming and extreme events. Over East China, where the adjacent ocean exhibits stronger‐than‐global mean warming, the local TS and both the strength and frequency of heat extremes keep increasing continuously. The extreme precipitation intensity increases even more rapidly compared to the change of heat extremes. In stark contrast, TS and heat extremes intensity over northern Eurasia decrease in both the 1.5 °C and 1.5 °C OS cases, except that the extreme precipitation experiences little change. We find that the most vulnerable period over northern Eurasia is the transition period, in which TS increases till its maximum and then decreases. The heat extremes during the transition period are also stronger and more frequent compared to the end of the 21st century over northern Eurasia.