A conventional scanning FT-IR spectrometer is used to measure the blackbody radiation through a rapidly moving pinhole in an experiment simulating a dying hot particle. The effects and errors from source movements are analyzed and verified through experiments. The importance of the scanning velocity, phase-correction method, and temperature variations during scanning is investigated. It is shown that a calibration of the system at one temperature is sufficient for accurate spectral radiance and temperature measurements throughout a broad temperature range. The temperature errors are reduced by a factor of 2-10 compared with results from a typical two-color pyrometer. A novel method is presented for measuring emission spectra from single moving particles passing the field of view of the spectrometer in a random manner.