We study the impact of relatively weak AGN feedback on the interstellar medium of intermediate and massive elliptical galaxies . We find that the AGN activity , while globally heating the ISM , naturally stimulates some degree of hot gas cooling on scales of several kpc . This process generates the persistent presence of a cold ISM phase , with mass ranging between 10 ^ { 4 } and \ga 5 \times 10 ^ { 7 } M _ { \odot } , where the latter value is appropriate for group centered , massive galaxies . Widespread cooling occurs where the ratio of cooling to free-fall time before the activation of the AGN feedback satisfies t _ { cool } / t _ { ff } \la 70 , that is we find a less restrictive threshold than commonly quoted in the literature . This process helps explaining the body of observations of cold gas ( both ionized and neutral/molecular ) in Ellipticals and , perhaps , the residual star formation detected in many early-type galaxies . The amount and distribution of the off-center cold gas vary irregularly with time . The cold ISM velocity field is irregular , initially sharing the ( outflowing ) turbulent hot gas motion . Typical velocity dispersions of the cold gas lie in the range 100 - 200 km s ^ { -1 } . Freshly generated cold gas often forms a cold outflow and can appear kinematically misaligned with respect to the stars . We also follow the dust evolution in the hot and cold gas . We find that the internally generated cold ISM has a very low dust content , with representative values of the dust-to-gas ratio of 10 ^ { -4 } -10 ^ { -5 } . Therefore , this cold gas can escape detection in the traditional dust-absorption maps .