Changes in Earth's outgoing radiance are expected to affect the thermal equilibrium of spaceborne instruments, and to produce detectable variations of satellite on-board temperatures (OBTs). In this study, temperatures of the Global Ozone Monitoring Experiment during the period July 1995--July 2004 have been analysed. Results show that GOME temperatures are influenced by solar flux variations and strongly driven by radiation fluxes from the Earth. The long-term behaviour of the GOME OBT is characterized by periodicities related to orbital and atmospheric phenomena, and by a steady increase, starting from year 1998. The behaviour of OBTs is consistent with the evolution of the observed shortwave radiative forcing from earthshine observations. The advantage of this technique resides in its simplicity. The proposed approach could be applied to all previous, current and future satellite instruments with thermal characteristics similar to GOME, providing a long time series of a proxy indicator of Earth climate.