The high computational cost of Global Climate Models (GCMs) is a problem that limits their use in many areas. Recently an inverse climate modeling (InvCM) method, which fixes the global mean sea surface temperature (SST) and evolves the CO₂ mixing ratio to equilibrate climate, has been implemented in a cloud-resolving model. In this article, we apply InvCM to ExoCAM GCM aquaplanet simulations, allowing the SST pattern to evolve while maintaining a fixed global-mean SST. We find that InvCM produces the same climate as normal slab-ocean simulations but converges an order of magnitude faster. We then use InvCM to calculate the equilibrium CO₂ for SSTs ranging from 290 to 340 K at 1 K intervals and reproduce the large increase in climate sensitivity at an SST of about 315 K at much higher temperature resolution. The speedup provided by InvCM could be used to equilibrate GCMs at higher spatial resolution or to perform broader parameter space exploration in order to gain new insight into the climate system. Additionally, InvCM could be used to find unstable and hidden climate states, and to find climate states close to bifurcations such as the runaway greenhouse transition.