Though primarily driven by insolation changes associated with well-known variations in Earth's astronomical parameters, the response of the climate system during interglacials includes a diversity of feedbacks involving the atmosphere, ocean, sea ice, vegetation and land ice. A thorough multimodel- data comparison is essential to assess the ability of climate models to resolve interglacial temperature trends and to help in understanding the recorded climatic signal and the underlying climate dynamics. We present the first multi-model-data comparison of transient millennial-scale temperature changes through two intervals of the Present Interglacial (PIG; 8-1.2 ka) and the Last Interglacial (LIG; 123-116.2 ka) periods. We include temperature trends simulated by 9 different climate models, alkenone-based temperature reconstructions from 117 globally distributed locations (about 45% of them within the LIG) and 12 ice-core-based temperature trends from Greenland and Antarctica (50% of them within the LIG). The definitions of these specific interglacial intervals enable a consistent inter-comparison of the two intervals because both are characterised by minor changes in atmospheric greenhouse gas concentrations and more importantly by insolation trends that show clear similarities. Our analysis shows that in general the reconstructed PIG and LIG Northern Hemisphere mid-to-high latitude cooling compares well with multi-model, mean-temperature trends for the warmest months and that these cooling trends reflect a linear response to the warmest-month insolation decrease over the interglacial intervals. The most notable exception is the strong LIG cooling trend reconstructed from Greenland ice cores that is not simulated by any of the models. A striking model-data mismatch is found for both the PIG and the LIG over large parts of the mid-to-high latitudes of the Southern Hemisphere where the data depicts negative temperature trends that are not in agreement with near zero trends in the simulations. In this area, the positive local summer insolation trend is counteracted in climate models by an enhancement of the Southern Ocean summer sea-ice cover and/or an increase in Southern Ocean upwelling. If the general picture emerging from reconstructions is realistic, then the model-data mismatch in mid and high Southern Hemisphere latitudes implies that none of the models is able to resolve the correct balance of these feedbacks, or, alternatively, that interglacial Southern Hemisphere temperature trends are driven by mechanisms which are not included in the transient simulations, such as changes in the Antarctic ice sheet or meltwater-induced changes in the overturning circulation.