It is well known that the classical Spitzer–Harm–Braginskii expression for the parallel plasma heat flux breaks down in the long mean free path limit, relevant to many practical applications, most crucially power exhaust via the tokamak scrape-off layer (SOL). This problem is usually addressed by limiting the heat flux to some fraction of the free streaming value, with constants of proportionality ασ, where σ ∊ {e,i}, ranging from 0.03 to 3. The following paper presents a brief overview of the problem, compares the results of various kinetic studies, suggests the optimal values of ασ for use in plasma–fluid codes, and examines the impact of these values on 2D SOL simulations using the EDGE2D transport code. In this context, gyro-kinetic parallel heat flux expressions for both electrons and ions are derived from the generalized transport equations—an improved version of Grad's 21-moment approach—and their implications to tokamak modelling are discussed.