The 35 W D2 automotive headlight lamp with an electrode gap of around 4 mm is a well known example of a short-arc high-intensity discharge (HID) lamp. It has a filling of xenon, mercury, and sodium/scandium iodide and is driven by a rectangular-wave current of 0.4 A, 400 Hz. Other fields of application of HID lamps are video projection (UHP), street and industrial lighting, floodlighting, etc. Due to their small size and short timescales, HID lamps are often experimentally difficult to investigate or even inaccessible. Thus modelling gets more and more important. The challenges in modelling such lamps are e.g. the important plasma–electrode interaction, the time dependence (electrodes change with 400 Hz from anode to cathode phase and vice versa in the case of D2 lamps), and the complex plasma composition (Xe, Hg, NaI, ScI₃ in the case of D2 lamps). Additionally the electrodes might change their well-defined tip geometry during operation, causing substantial changes in electrode temperature or electrode fall voltages. This paper intends to address all these questions and compare results of numerical simulations with measurements of plasma and electrode temperatures. Special focus is directed towards the important electrode–plasma interaction, which, even after seven decades of HID lamps, has not been understood satisfactorily. The results presented in this paper are very important for a better understanding of dc and ac HID lamps including the treatment of complex plasma compositions, the choice of the work functions, and the effect of different electrode geometries. Furthermore the results of the numerical simulations will lead to improved or new HID lamps.