The Antarctic plateau provides the best terrestrial sites for infrared and sub-millimetre astronomy. In this paper we examine the relative importance of temperature, aerosol content and precipitable water vapour to determine which parameters have the greatest influence on atmospheric transmission and sky brightness. We use the atmospheric modelling program, MODTRAN, to model the observed sky spectrum at the South Pole from the near-IR to the sub-millimetre. We find that temperature and aerosol content determine the quality of near-IR observing conditions, aerosol content is the determining factor in the mid-IR up to 20m, while at longer wavelengths, including the sub-millimetre, it is the water vapour content that matters. Finding a location where aerosol levels are minimised is a key constraint in determining the optimum site on the Antarctic plateau for an infrared observatory.