[en] Amplification of a radially polarized beam from an Yb:YAG seed laser at 1030 nm in a very-large-core triple-clad ytterbium-doped fiber configured as a thermally guiding fiber rod amplifier is demonstrated. The amplifier yielded a maximum output power of 10.7 W (limited by available pump power) with corresponding single-pass gain of 6.4 dB, while the radial polarization purity was maintained over the full range of pump power with a measured polarization extinction ratio of 100:1. The amplified output beam displayed the characteristic donut-shaped intensity profile with negligible beam distortion as evidenced by a measured beam propagation factor (M²) of 2.1 ± 0.1. A simplified model for propagation of a radially polarized beam in a thermally guided fiber rod is developed to provide insight into the underlying design principles and to establish a strategy for scaling output power. The power scaling limitations of this approach are considered.