Experiments on rotating annuli that are differentially heated in the radial direction have largely contributed to a better understanding of baroclinic instabilities. This configuration creates waves at a laboratory scale that are related to atmospheric circulations. Pioneer studies in baroclinic tanks have shown that experiments with low aspect ratios are more suitable to reproduce small-scale inertia gravity waves, but these tanks have a larger free surface, which leads to higher interactions with their surrounding environment. Considering the heat transferred through the free surface, the present work investigates its impacts on the baroclinic instability using direct numerical simulations (DNS).