Solar wind electrons are observed often to consist of two components: a core and a halo. The anisotropies and relative average speed of these two components correspond to a heat flux that has the potential to excite several different electromagnetic instabilities; wave-particle scattering by the resulting enhanced fluctuations can limit this heat flux. This manuscript describes theoretical studies using the linear Vlasov dispersion equation for drifting bi-Maxwellian component distributions in a homogeneous plasma to examine the threshold of the whistler heat flux instability. Expressions for this threshold are obtained from two different parametric baselines: a local model that yields scalings as functions of local dimensionless plasma parameters, and a global model based on average electron properties observed during the in-ecliptic phase of the Ulysses mission. The latter model yields an expression for the heat flux at threshold of the whistler instability as a function of heliospheric radius that scales in the same way as the average heat flux observed from Ulysses and that provides an approximate upper bond for that same quantity. This theoretical scaling is combined with the observational results to yield a semiempirical closure relation for the average electron heat flux in the solar wind between 1 and 5 AU. ¿ American Geophysical Union 1994