The behavior of sensible heat flux H with stability parameter ζ in the stable atmospheric surface layer is analyzed within the framework of Monin‐Obukhov similarity theory (MOST). Using MOST equations, H is expressed as a function of ζ and wind shear ∂U/∂z. A systematic mathematical analysis is carried out to analyze the behavior of H with ζ utilizing the linear as well as various nonlinear empirical functional forms of the similarity functions. In case of linear form, for a given value of H, two different values of ζ along with the “downward heat flux maximum” with a unique critical point are found to occur. However, for the other selected empirical similarity functions, more than two values of ζ having the same magnitude of H may occur suggesting the existence of multiple critical points. Further, the observational variation of H with ζ is analyzed using data from three different sites. Data suggest the existence of two different stability regimes for the same magnitude of heat flux. However, the data do not support the existence of multiple values of ζ for the same magnitude of H, as predicted by MOST with the other selected empirical forms of similarity functions. This suggests that the phenomenon of existence of downward heat flux maximum, as predicted by MOST equations, depends on the functional form of the similarity functions, and it appears to break down for some selected empirical forms of similarity functions under very stable conditions.