Abstract Tokamak edge (scrape-off layer (SOL)) plasmas can exhibit non-local transport in the direction parallel to the magnetic field due to steep temperature gradients. This effect along with its consequences has been explored at equilibrium for a range of conditions, from sheath-limited to detached, using the 1D kinetic electron code SOL-KiT, where the electrons are treated kinetically and compared to a self-consistent fluid model. Line-averaged suppression of the kinetic heat flux (compared to Spitzer-Härm) of up to 50% is observed, contrasting with up to 98% enhancement of the sheath heat transmission coefficient, γ e . Simple scaling laws in terms of basic SOL parameters for both effects are presented. By implementing these scalings as corrections to the fluid model, we find good agreement with the kinetic model for target electron temperatures. It is found that the strongest kinetic effects in γ e are observed at low-intermediate collisionalities, and tend to increase (keeping upstream collisionality fixed) at increasing upstream densities and temperatures. On the other hand, the heat flux suppression is found to increase monotonically as upstream collisionality decreases. The conditions simulated encompass collisionalities relevant to current and future tokamaks.