We present a simple design of a balloon-borne infrared spectral photometer that can be built and used by undergraduate students to perform an experiment demonstrating the atmospheric greenhouse effect. The experiment demonstrates that the Earth radiates heat to space in the infrared region but that the radiation at the top of the atmosphere has a much lower effective radiation temperature than at the surface of the Earth, which is the essence of the greenhouse effect. The experiment also demonstrates that the greenhouse effect is much more pronounced in molecular absorption bands than in the so-called infrared window. The thrill of putting together a balloon experiment aside, students performing this experiment also gained experience in practical applications of Planck's law.