© Author(s) 2014. During the Archaean, the Sun's luminosity was 18 to 25% lower than the present day. One-dimensional radiative convective models (RCM) generally infer that high concentrations of greenhouse gases (CO2, CH4) are required to prevent the early Earth's surface temperature from dropping below the freezing point of liquid water and satisfying the faint young Sun paradox (FYSP, an Earth temperature at least as warm as today). Using a one-dimensional (1-D) model, it was proposed in 2010 that the association of a reduced albedo and less reflective clouds may have been responsible for the maintenance of a warm climate during the Archaean without requiring high concentrations of atmospheric CO2 (pCO2). More recently, 3-D climate simulations have been performed using atmospheric general circulation models (AGCM) and Earth system models of intermediate complexity (EMIC). These studies were able to solve the FYSP through a large range of carbon dioxide concentrations, from 0.6 bar with an EMIC to several millibars with AGCMs. To better understand this wide range in pCO2, we investigated the early Earth climate using an atmospheric GCM coupled to a slab ocean. Our simulations include the ice-albedo feedback and specific Archaean climatic factors such as a faster Earth rotation rate, high atmospheric concentrations of CO2 and/or CH4, a reduced continental surface, a saltier ocean, and different cloudiness. We estimated full glaciation thresholds for the early Archaean and quantified positive radiative forcing required to solve the FYSP. We also demonstrated why RCM and EMIC tend to overestimate greenhouse gas concentrations required to avoid full glaciations or solve the FYSP. Carbon cycle-climate interplays and conditions for sustaining pCO2 will be discussed in a companion paper.