The far-infrared spectroscopy of the troposphere (FIRST) instrument is a Fourier-transform spectrometer developed to measure the Earth's thermal emission spectrum with a particular emphasis on the far-infrared. FIRST has observed the atmosphere from both the ground looking up and from a high-altitude balloon looking down. A recent absolute laboratory calibration of FIRST under ground-like operating conditions showed accuracy to better than 0.3 K at near-ambient temperatures (270-325 K) but reduced accuracy at lower temperatures. This paper presents calibration results for balloon-flight conditions using a cold blackbody to simulate the space view used for on-board calibration. An unusual detector nonlinearity was discovered and corrected, and stray light was measured and removed. Over most of the range of Earth scene temperatures (205-300 K), the accuracy of FIRST is 0.35-0.15 K (one sigma).