Due to the constant size reduction, single-donor-based nanowire transistors receive an increasing interest from the semi-conductor industry. In this work we theoretically investigate the coupled influence of electron-phonon scattering, temperature and size (cross-section and channel length) on the properties of such systems. The aim is to determine under what conditions the localized character of the donor has a remarkable impact on the current characteristics. We use a quantum non-equilibrium Green's function approach in which the acoustic electron-phonon scattering is treated through local self-energies. We first show how this widely used approach, valid at high temperatures, can be extended to lower temperatures. Our simulations predict a hysteresis in the current when reducing the temperature down to 150 K. We also find that acoustic phonons degrade the current characteristics while their optical counterparts might have a beneficial impact with an increase of the ON-current. Finally we discuss the influence of nanowire length and cross-section and emphasize the complexity of precisely controlling the dopant level at room temperature. (C) 2016 Elsevier Ltd. All rights reserved.