We investigated thermospheric hydrogen response to increase in greenhouse gases and the dependence of this response to solar activity, using a global mean version of the National Center for Atmospheric Research Thermosphere‐Ionosphere‐Mesosphere‐Electrodynamics General Circulation Model. We separately doubled carbon dioxide (CO2) and methane (CH4) to study the influence of temperature and changes to source species for hydrogen. Our results indicate that both CO2 cooling and CH4 changes to the source species for hydrogen lead to predicted increases in the upper thermospheric hydrogen density. At 400 km, hydrogen increases ~30% under solar maximum and ~25% under solar minimum responding to doubling of CH4, indicating that hydrogen response to the source variation due to CH4 increase is relatively independent of solar activity. On the other hand, hydrogen response to doubling of CO2 highly depends on solar activity. At 400 km, doubling of CO2 results in an ~7% hydrogen increase at solar maximum, whereas it is ~25% at solar minimum. Consequently, at solar maximum, the predicted ~40% increase in atomic hydrogen in the upper thermosphere is primarily due to the source variation as a result of doubling of CH4, whereas at solar minimum, both cooling due to doubling of CO2 and the source variation due to doubling of CH4 have commensurate effects, resulting in an approximate 50% increase in the modeled upper thermospheric hydrogen.