The reduction of the thermal conductivity induced by nano-patterning is one of the major approaches for tailoring thermoelectric material properties. In particular, the role of surface roughness and morphology is under debate. Here, we choose two individual bismuth telluride nanowires (NWs), one with a strong diameter variation between 190 nm and 320 nm (NW1) and the other of 187 nm diameter with smooth sidewalls (NW2). Both serve as model systems for which bulk properties are expected if surface properties do not contribute. We investigate the role of the diameter variation by means of a combined full-thermoelectrical, structural and chemical characterization. By transmission electron microscopy the structure, chemical composition and morphology were determined after the thermoelectrical investigation. The NWs showed an oriented growth along the {[}110] direction and the same composition. The Seebeck coefficients of both NWs are comparable to each other. The electrical conductivity of both NWs exceeds the bulk value indicating the presence of a topological surface state. Whereas the thermal conductivity of NW2 compares to the bulk, the thermal conductivity of NW1 is about half of NW2 which is discussed with respect to its distinct diameter variation.