The past climate reconstruction in different spatial and temporal scales using proxy records can provide a reliable basis for assessing climate model simulations, but also for exploring the present and future climate change regime. In this paper, we use 501 global proxy records published by past global change (PAGES) 2k network working group, including 418 tree-ring chronologies, 29 ice-cores, 13 corals, 2 speleothems, 34 lake/sea sediments, 1 historical document, and 4 instrumental records. Based on these explicit temperature-sensitive proxies with accurate dating, we reconstruct the spatial pattern of global temperature with decadal resolution over the past millennium using the hybrid frequency-domain Regularized Expectation Maximization procedure, and then, analyze the similarities and differences of typical centennial warm periods between the Medieval Warm Period (MWP) in 950~ 1250A.D. and the Current Warm Period (CWP) in 1901 ~ 2000A.D., and typical 30 years warm periods among the MWP, Little Ice age (LIA) and CWP. Results show that the temperature anomalies during the CWP in most of regions are higher than ones during the MWP, especially in Eurasia, North America, Eastern Pacific, South Atlantic and Indian Oceans. The temperature anomalies in the last 30 years (1971 ~ 2000A.D.) of the CWP are also distinctly higher than in the warmest 30 years (972 ~ 1001 A.D.) of the MWP and the LIA (1608 ~ 1637A.D.) except for North Atlantic. The temperature anomalies of the warmest 100 years (950 ~ 1049A.D.) of the MWP have no significant difference in most of regions compared to the CWP. This indicates that temperature anomalies during the warmest century of the MWP are comparable to those in amplitude during the CWP in most of regions on a centennial timescale, but on a decadal timescale, the warming in the last 30 years are unprecedented compared to the past two diagnostic periods. It is noteworthy that, the high-latitude North Atlantic sea surface temperature anomalies in the LIA and MWP on decadal to centurial timescales are higher than those in the CWP. The mechanism may be that the high solar radiation and weak volcanic activity induce the increasing equatorial Pacific sea surface temperature gradient through a thermostat mechanism during the MWP. This process strengthens the trade winds and helps La Nina-like continued. Classic La Nina condition causes the Southern Hemisphere westerlies move to south, and increases saltwater exchange between the Indian Ocean and South Atlantic,and results in strengthening the Atlantic meridional overturning circulation (AMOC). The outcome is warm sea surface temperature anomalies in high-latitude North Atlantic. Moreover, the La Nina-like condition impacts Hadley circulation in equatorial Atlantic and spreads down through the stratosphere, which affect the North Atlantic Oscillation (NAO). This also results in warm sea surface temperature anomalies in high-latitude North Atlantic. The AMOC from the MWP to the LIA from strong to weak is mainly affected by the weaker solar radiation and stronger volcanic activity for a transition, leading to decreases in the North Atlantic sea surface temperature. However, the AMOC mainly responding to the rapid increase in greenhouse gas in the CWP is weakened, leading to cold North Atlantic sea surface temperature anomalies.