We report a systematic study of the dependence of image-potential states on surface temperature and oxygen adsorption on Cu(100) using two-photon photoemission spectroscopy. The binding energy of the n=1 image-potential state is found to be insensitive to temperature, in agreement with inverse-photoemission measurements. In the temperature range 300--963 K, the image-peak amplitude is found to have a weak temperature dependence. The exposure of Cu(100) to oxygen (1.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ Torr s) reduces the intensity of the image-potential peak and causes a shift of the position of this peak toward higher kinetic energy by an amount comparable to the change in the work function. A technique is described for eliminating space-charge effects, which can be a problem in pulsed-laser two-photon measurements.