The Earth's climate system is driven by a complex interplay of internal chaotic dynamics and natural and anthropogenic external forcing. Recent instrumental data have shown a remarkable degree of asynchronicity between Northern Hemisphere and Southern Hemisphere temperature fluctuations, thereby questioning the relative importance of internal versus external drivers of past as well as future climate variability. However, large-scale temperature reconstructions for the past millennium have focused on the Northern Hemisphere, limiting empirical assessments of inter-hemispheric variability on multi-decadal to centennial timescales. Here, we introduce a new millennial ensemble reconstruction of annually resolved temperature variations for the Southern Hemisphere based on an unprecedented network of terrestrial and oceanic palaeoclimate proxy records. In conjunction with an independent Northern Hemisphere temperature reconstruction ensemble, this record reveals an extended cold period (1594-1677) in both hemispheres but no globally coherent warm phase during the pre-industrial (1000-1850) era. The current (post-1974) warm phase is the only period of the past millennium where both hemispheres are likely to have experienced contemporaneous warm extremes. Our analysis of inter-hemispheric temperature variability in an ensemble of climate model simulations for the past millennium suggests that models tend to overemphasize Northern Hemisphere-Southern Hemisphere synchronicity by underestimating the role of internal ocean-atmosphere dynamics, particularly in the ocean-dominated Southern Hemisphere. Our results imply that climate system predictability on decadal to century timescales may be lower than expected based on assessments of external climate forcing and Northern Hemisphere temperature variations alone.