Understanding the origin of stellar masses is a key problem in astrophysics. In the solar neighborhood, the mass distribution of stars follows a seemingly universal pattern. In the centre of the Milky Way, however, there are indications for strong deviations and the same may be true for the nuclei of distant starburst galaxies. Here we present the first numerical hydrodynamical calculations of stars formed in a molecular region with chemical and thermodynamic properties similar to those of warm and dusty circum-nuclear starburst regions. The resulting IMF is top-heavy with a peak at 15 Mo, a sharp turn-down below 7 Mo and a power-law decline at high masses. We find a natural explanation for our results in terms of the temperature dependence of the Jeans mass, with collapse occuring at a temperature of 100 K and an H2 density of a few * 105 cm^-3, and discuss possible implications for galaxy formation and evolution.