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Ultrashort laser pulses are widely used for transient field-free molecular orientation -- a phenomenon important in chemical reaction dynamics, ultrafast molecular imaging, high harmonics generation, and attosecond science. However, significant molecular orientation usually requires rotationally cold molecules, like in rarified molecular beams, because chaotic thermal motion is detrimental to the orientation process. Here we propose to use the mechanism of the echo phenomenon previously observed in hadron accelerators, free-electron lasers, and laser-excited molecules to overcome the destructive thermal effects and achieve efficient field-free molecular orientation at high temperatures. In our scheme, a linearly polarized short laser pulse transforms a broad thermal distribution in the molecular rotational phase space into many separated narrow filaments due to the nonlinear phase mixing during the post-pulse free evolution. Molecular subgroups belonging to individual filaments have much-reduced dispersion of angular velocities. They are rotationally cold, and a subsequent moderate terahertz (THz) pulse can easily orient them. The overall enhanced orientation of the molecular gas is achieved with some delay, in the course of the echo process combining the contributions of different filaments. Our results demonstrate that the echo-enhanced orientation is an order of magnitude higher than that of the THz pulse alone. The mechanism is robust -- it applies to different types of molecules, and the degree of orientation is relatively insensitive to the temperature. The laser and THz pulses used in the scheme are readily available, allowing quick experimental demonstration and testing in various applications. Breaking the phase space to individual filaments to overcome hindering thermal conditions may find a wide range of applications beyond molecular orientation.