To repeat @Malijam comment, by `thermal motion` it is referring to the "random giggling" of molecules.
Temperature difference is nothing but a change in the frequency at which molecule move randomly. This movement has no specific direction. If a given molecule is prevented from moving into one specific direction (due to attachement to another molecule) but allowed to move into another, then the molecule will move directionally pushed by nothing but its thermal kinetic. This create a so called thermal ratchet.