This work provides an in-depth study of how the thermal conductivity of stoichiometric  Bi2Te3 nanowires becomes affected when reducing its diameter from an experimental and theoretical point of view. The thermal conductivity was observed to decrease more than 70% (from 1.78 ± 0.46 W K-1 m-1 to 0.52 ± 0.35 W K-1 m-1) when the diameter of the nanowire was reduced one order of magnitude (from 300 nm to 25 nm). The Kinetic-Collective model was used to understand such a reduction, which can be explained by the impact that surface scattering has in acoustic phonons. The smaller the diameter of the nanowires is, the larger the alteration in the mean free path of the low-frequency phonons is. The model agrees well with the experimental data, and the reduction in the thermal conductivity of the nanowires can be explained in terms of an increment of phonon scattering.