In one example, the method disclosed herein includes forming a fin comprised of a semiconducting material, wherein the fin has a first, as-formed cross-sectional configuration, forming a sacrificial gate structure above the fin, forming sidewall spacers adjacent at least a portion of the sacrificial gate structure and removing the sacrificial gate structure to thereby define a gate cavity that exposes a portion of the fin. The method also includes the steps of performing a fin reflow process on the exposed portions of the fin to define a nanowire structure having a cross-sectional configuration that is different from the first cross-sectional configuration and forming a replacement gate structure in the gate cavity and at least partially around the nanowire structure.