As Earth warms, the tropopause is expected to rise, but predictions of its temperature change are less certain. One theory ties tropopause temperature to outgoing longwave radiation (OLR), but this contradicts simulations that exhibit a Fixed Tropopause Temperature (FiTT) even as OLR increases. Another theory ties tropopause temperature to upper tropospheric moisture, but is not precise enough to make quantitative predictions. Here, we argue that tropopause temperature, defined by where radiative cooling becomes negligible, is set by water vapor’s maximum spectroscopic absorption and Clausius-Clapeyron scaling. This “thermospectric constraint’ makes quantitative predictions for tropopause temperature that are borne out in single column and general circulation model experiments where the spectroscopy is modified and the tropopause changes in response. This constraint underpins the FiTT hypothesis, shows how tropopause temperature can decouple from OLR, suggests a way to relate the temperatures of anvil clouds and the tropopause, and shows how spectroscopy manifests in Earth’s general circulation.