The dependence of the growth rate and the threshold level of the whistler heat flux instability in the solar wind at 1 AU on the shape of the velocity distribution function and on the electron halo temperature anisotropy is examined by using a drifted bi-Lorentzian distribution function. We find that for a given set of plasma parameters the maximum growth rate increases sharply with increasing slope of the halo electron velocity distribution and that the whistler instability threshold level increases sharply with increasing halo temperature anisotropy. In view of the sensitivity of the whistler instability threshold level to details of the shape of halo electron distribution functions it is not now possible to decide unambiguously if the whistler mode regulates the interplanetary heat flux some of the time at 1 AU, but it remains a strong candidate.