Improving upon our purely dynamical work, we present three-dimensional simulations of the atmospheric circulation on Earth-like (exo)planets and hot Jupiters using the Geophysical Fluid Dynamics Laboratory (GFDL)-Princeton Flexible Modelling System (fms). As the first steps away from the dynamical benchmarks of Heng, Menou & Phillipps, we add dual-band radiative transfer and dry convective adjustment schemes to our computational set-up. Our treatment of radiative transfer assumes stellar irradiation to peak at a wavelength shorter than and distinct from that at which the exoplanet re-emits radiation (‘shortwave’ versus ‘longwave’), and also uses a two-stream approximation. Convection is mimicked by adjusting unstable lapse rates to the dry adiabat. The bottom of the atmosphere is bounded by a uniform slab with a finite thermal inertia. For our models of hot Jupiter, we include an analytical formalism for calculating temperature–pressure profiles, in radiative equilibrium, which accounts for the effect of collision-induced absorption via a single parameter. We discuss our results within the context of the following: the predicted temperature–pressure profiles and the absence/presence of a temperature inversion; the possible maintenance, via atmospheric circulation, of the putative high-altitude, shortwave absorber expected to produce these inversions; the angular/temporal offset of the hotspot from the substellar point, its robustness to our ignorance of hyperviscosity and hence its utility in distinguishing between different hot Jovian atmospheres; and various zonal-mean flow quantities. Our work bridges the gap between three-dimensional simulations which are purely dynamical and those which incorporate multiband radiative transfer, thus contributing to the construction of a required hierarchy of three-dimensional theoretical models.