One-dimensional alignment of molecules in the adiabatic limit, where the pulse duration greatly exceeds the molecular rotational periods, is studied experimentally. Four different asymmetric top molecules (iodobenzene, p-diiodobenzene, 3,4-dibromothiophene, and 4,4'-dibromobiphenyl), rotationally cooled through a high pressure supersonic pulsed valve, are aligned by a 9-ns-long pulse. Their orientations are measured through Coulomb explosion, induced by a 130-fs-long pulse, and by recording the direction of the recoiling ions. The paper focuses on the crucial role of the initial rotational temperature for the degree of alignment. In particular, we show that at molecular temperatures in the 1 K range very strong alignment is obtained already at intensities of a few times 10(11) W/cm2 for all four molecules. At the highest intensities (approximately 10(12) W/cm2) the molecules can tolerate without ionizing <cos2 theta> >or=0.92 in the case of iodobenzene. This is the strongest degree of alignment ever reported for any molecule.