We address the problem of calculating the parallel electron heat condu
ction in a tokamak scrape off layer with non-negligible mean free path
. We develop a model distribution function based on pieces of Fokker-P
lanck solutions, containing: a local Maxwellian at low energies, a mod
ified Spitzer-Harm distribution at energies below where the mean free
path equals the distance to the nearest wall, a bounce-averaged distri
bution at higher energies up to the confining potential energy, a fill
ed-in outgoing loss-cone distribution at still higher energies, and fi
nally an empty loss region at energies such that the mean free path ex
ceeds the length of the field line. The model is compared with Monte C
arlo simulations.