======================================================================= ==> In this proposal, more time is being requested for TLEBERTR.ISM_AGB ======================================================================= The large luminosity of Asymptotic Giant Branch (AGB) stars (in most cases from 5 10^3 to 2 10^4 solar luminosity) potentially makes them important heating sources of the Interstellar Medium (ISM) that surrounds them. Their spectra peak at wavelengths larger than 1 micron, and the dominant effect is through radiative heating of the large grain component of the IS dust. The aim of this proposal is to study the effect of the radiative heating of IS dust by AGB stars and the filling factor of the general ISM. We propose to map the ISM in volumes of 10 cubic parsecs with a typical spatial resolution of 0.2 parsecs around sources at a typical distance of 1 kpc from the Sun. For this, we will use ISOPHOT with PHT-C100 and C_60/C_90. The fields will have a size of 7 arcmin by 7 arcmin and will be centered at 5 arcmin from the heating sources. This programme will give new insights on the small scale structure of the ISM and on dust properties in very different galactic environments (from the disk to the halo) at distances from the Sun ranging from 500 pc to 1500 pc, with a spatial resolution of 0.1 to 0.3 pc. It has been started successfully with the observations of two fields for the initial proposal (ISM_AGB). The proposed sample of 12 fields will complement the sample of 10 fields which is already in priority 2 (and 10 fields in priority 3) from this initial proposal. We estimate that we will obtain 12 fields from ISM_AGB. In total, with 24 fields (12 on ISM_AGB + 12 on ISM_AGB2), we will probe the ISM in a total volume of 200 cubic parsecs and derive an unbiased evaluation of the ISM filling factor.