Solar brightness temperature data obtained at 34.9 km during a balloon flight from the Canadian Space Research Facility on August 28, 1982 are analyzed. A servocontrolled telescope capable of solar image scanning, a Michelson interferometer with 0.015/cm apodized resolution, and an in-flight radiometric calibration source were used to obtain the temperature data. Interferograms and spectra from the sun, the sky background, and blackbody at its equilibrium temperature of 1165 K are studied, and values of solar brightness temperature are derived from the spectra. The relation between solar brightness temperature and wave number is examined. The effects of systematic error on the solar temperature data are investigated. An intrinsic temperature minimum of 4170 K and an observable minimum of 4300 K were obtained. The temperature values are compared with the predictions of Vernazza et al. (1981), and good correlation is detected. 24 references.