We report on an approach for a compact ultrafast thin-disk multipass laser amplifier making use of a highly compact geometric folding scheme. The setup is also suitable to minimize the effects caused by natural convection of hot air in front of the thin-disk on the amplified laser beam as it facilitates to orient the laser disk with its axis in the vertical direction. The efficacy of this approach is analyzed with finite-element method simulations of the heated laser crystal in ambient air with different orientations of the thin laser disk. The experiments confirm a significant improvement of the amplifier performance in terms of stability and an increase of the output power with nearly diffraction-limited beam quality (M²  ≤  1.4) by a factor of 3 with respect to the conventional orientation of the laser disk.