The last interglacial (LIG), also identified to the Eemian in Europe, began at approximately 130 kyr BP and ended at about 115 kyr BP (before present). More and more proxy-based reconstructions of the LIG climate are becoming more available even though they remain sparse. The major climate forcings during the LIG are rather well known and therefore models can be tested against paleoclimatic data sets and then used to better understand the climate of the LIG. However, models are displaying a large range of responses, being sometimes contradictory between them or with the reconstructed data. Here we would like to investigate causes of these differences. We focus on a single climate model, LOVECLIM, and we perform transient simulations over the LIG, starting at 135 kyr BP and run until 115 kyr BP. With these simulations, we test the role of the surface boundary conditions (the time-evolution of the Northern Hemisphere (NH) ice sheets) on the simulated LIG climate and the importance of the parameter sets (internal to the model, such as the albedos of the ocean and sea ice), which affect the sensitivity of the model. The magnitude of the simulated climate variations through the LIG remains too low compared to reconstructions for climate variables such as surface air temperature. Moreover, in the North Atlantic, the large increase in summer sea surface temperature towards the peak of the interglacial occurs too early (at similar to 128 kyr BP) compared to the reconstructions. This feature as well as the climate simulated during the optimum of the LIG, between 131 and 121 kyr BP, does not depend on changes in surface boundary conditions and parameter sets. The additional freshwater flux (FWF) from the melting NH ice sheets is responsible for a temporary abrupt weakening of the North Atlantic meridional overturning circulation, which causes a strong global cooling in annual mean. However, the changes in the configuration (extent and albedo) of the NH ice sheets during the LIG only slightly impact the simulated climate. Together, configuration of and FWF from the NH ice sheets greatly increase the magnitude of the temperature variations over continents as well as over the ocean at the beginning of the simulation and reduce the difference between the simulated climate and the reconstructions. Lastly, we show that the contribution from the parameter sets to the climate response is actually very modest.