From 10 to 8 ka BP (thousand years before present), paleoclimate records show an atmospheric and oceanic cooling in the high latitudes of the Southern Hemisphere. During this interval, temperatures estimated from proxy data decrease by 0.8 degrees C over Antarctica and 1.2 degrees C over the Southern Ocean. In order to study the causes of this cooling, simulations covering the early Holocene have been performed with the climate model of intermediate complexity LOVECLIM constrained to follow the signal recorded in climate proxies using a data assimilation method based on a particle filtering approach. The selected proxies represent oceanic and atmospheric surface temperature in the Southern Hemisphere derived from terrestrial, marine and glaciological records. Two mechanisms previously suggested to explain the 10-8 ka BP cooling pattern are investigated using the data assimilation approach in our model. The first hypothesis is a change in atmospheric circulation, and the second one is a cooling of the sea surface temperature in the Southern Ocean, driven in our experimental setup by the impact of an increased West Antarctic melting rate on ocean circulation. For the atmosphere hypothesis, the climate state obtained by data assimilation produces a modification of the meridional atmospheric circulation leading to a 0.5 degrees C Antarctic cooling from 10 to 8 ka BP compared to the simulation without data assimilation, without congruent cooling of the atmospheric and sea surface temperature in the Southern Ocean. For the ocean hypothesis, the increased West Antarctic freshwater flux constrainted by data assimilation (+100 mSv from 10 to 8 ka BP) leads to an oceanic cooling of 0.7 degrees C and a strengthening of Southern Hemisphere westerlies (+6 %). Thus, according to our experiments, the observed cooling in Antarctic and the Southern Ocean proxy records can only be reconciled with the reconstructions by the combination of a modified atmospheric circulation and an enhanced freshwater flux.