In this work we examine the heating of the solar wind above the heliobase. Based on the discontinuous solar wind solutions of Shergelashvili et al. [1] we developed new quasi-discontinuous solar wind models in Westrich et al. [2]. First, we will present the basic concept of discontinuous solar wind solutions and the quasi-discontinuous solar wind models, which is basically equivalent to assuming a localized heating source above the heliobase in the case of a 1D quasi-adiabatic, radial expansion of a one-fluid solar wind. Furthermore, we will discuss the differences and the similarities of the discontinuous and quasi-discontinuous models. They contain strong gradients in their physical properties. Therefore, after a discussion of the characteristics of these solutions we will examine how heat conduction could weaken the discontinuities by explicitly including heat conduction in a two-fluid model. We will show that heat conduction is not strong enough to flatten the basic flow structure. As a result, the idea behind these models, i.e., that a damping of plasma waves near the transsonic point could produce such solar wind structures, remains reasonable.