Context: Recent 1.2-mm continuum observations have shown the giant H II region NGC 3576 to be embedded in the centre of an extended filamentary dust-cloud. The bulk of the filament away from the H II region contains a number of clumps seen only at (sub-)millimetre wavelengths. Infrared and radio observations of the central star cluster have uncovered evidence of sequential star-formation leading us to believe that the adjacent clumps may host massive protostellar objects at a very early stage of evolution. Aims: We have investigated the physical and chemical conditions in the dusty clumps with the goal of characterising their star-forming content. Methods: We have used the Australia Telescope Compact Array (ATCA) to image the cloud for the NH3 (1,1), (2,2) and (4,4) transitions, 22 GHz H2O masers, and 23 GHz continuum emission. The 70-m Tidbinbilla dish was used to estimate the total integrated intensity of NH3. We also utilised the 22-m Mopra antenna to map the region for the molecular lines 13CO (1 - 0), C18O (1 - 0), HCO+ (1 - 0), H13CO+ (1 - 0), CS (1 - 0) and N2H+ (1 - 0). Results: Emission from dense molecular gas follows the morphology of the 1.2-mm dust emission, except towards the central ionised region. The H II region is observed to be expanding into the molecular cloud, sweeping up a clumpy shell of gas, while the central star cluster is dispersing the molecular gas to the east. Analysis of the NH3 data indicates that temperature and linewidth gradients exist in the western arm of the filament. Temperatures are highest adjacent to the central H II region, indicating that the embedded cluster of young stars there is heating the gas. Six new H2O masers were detected in the arms of the filament, all associated with NH3 emission peaks, confirming that star-formation has begun within these cores. Core masses range from 5 to 516 Mȯ and most appear to be gravitationally bound. Complementary results by André et al. (2008) imply that seven cores will go on to form massive stars between 15 and 50 Mȯ. The large scale velocity structure of the filament is smooth, but at least one clump shows the signature of inward gas motions via asymmetries in the NH3 (1,1) line profiles. The same clump exhibits an enhanced abundance of N2H^+, which coupled with an absence of CO indicates depletion onto the dust grain surface. Conclusions: The HII region at the heart of NGC 3576 is potentially triggering the formation of massive stars in the bulk of the associated cloud.