Using large‐eddy simulations (LES) systematically has the potential to inform parameterizations of subgrid‐scale processes in general circulation models (GCMs), such as turbulence, convection, and clouds. Here we show how LES can be run to simulate grid columns of GCMs to generate LES across a cross section of dynamical regimes. The LES setup approximately replicates the thermodynamic and water budgets in GCM grid columns. Resolved horizontal and vertical transports of heat and water and large‐scale pressure gradients from the GCM are prescribed as forcing in the LES. The LES are forced with prescribed surface temperatures, but atmospheric temperature and moisture are free to adjust, reducing the imprinting of GCM fields on the LES. In both the GCM and LES, radiative transfer is treated in a unified but idealized manner (semigray atmosphere without water vapor feedback or cloud radiative effects). We show that the LES in this setup reaches statistically steady states without nudging to thermodynamic GCM profiles. The steady states provide training data for developing GCM parameterizations. The same LES setup also provides a good basis for studying the cloud response to global warming