In order to improve the presently used ad hoc flux limiter treatment of parallel heat flux transport in edge plasma fluid codes, here, we consider a generalized version of the Fourier law implementing a non-local kernel for the heat flux computation. The Bohm boundary condition at the wall is recovered, introducing a volumetric loss term representing the contribution of suprathermal particles to the energy out flux. As expected, this contribution is negligible in the strongly collisional regime, while it becomes more and more dominant for marginally and low-collisional regimes. In the second part of the paper, we consider a kinetic approach where collisions are considered using the multi-particle collision algorithm. Kinetic simulation results at medium and low collisionality are also reported.