Aims. We analyse SUMER spectral scans of a large sunspot within active region NOAA 10923, obtained on 14-15 November 2006, to determine the morphology and dynamics of the sunspot atmosphere at different heights/temperatures. Methods: The data analysed here consist of spectroheliograms in the continuum around 142.0 nm and in the Si iv 140.2 nm, O iii 70.3 nm, N iv 76.5 nm, and O iv 79.0 nm spectral lines. Gaussian-fitting of the observed profiles provides line-of-sight velocity and Doppler-width maps. Results: The data show an asymmetric downflow pattern compatible with the presence of the inverse Evershed flow in a region within roughly twice the penumbral radius at transition-region temperatures up to 0.18 MK. The motions, highly inhomogeneous on small scales, seem to occur in a collar of radially directed filamentary structures, with an average width less than the 1 Mm spatial resolution of SUMER and characterised by different plasma speeds. Assuming that the flows are directed along the field lines, we deduce that such field lines are inclined by 10 deg to 25 deg with respect to the solar surface.