This paper reports a second generation of radiation-balanced fiber laser and amplifier cooled internally using anti-Stokes fluorescence by pumping them at 1040 nm. In both devices the gain medium is a single-mode silica fiber with a core heavily doped with Yb<sup>3+</sup>, initially encapsulated in CaF<sub>2</sub> nanoparticles, and co-doped with Al to reduce quenching and increase the cooling efficiency. After optimization of its length (4.1 m) and its output coupler reflectivity (3.3%), the 1065- nm continuous-wave fiber laser has a threshold of 160 mW and a radiation-balanced (no net heat generation) output power of 192 mW, or nearly 70% higher than the previous radiation-balanced fiber laser. At its radiation-balanced point, its optical efficiency is 56.8%. The single-frequency, single-mode fiber amplifier, constructed with the same fiber, was optimum with a length of 6.8 m, and it had a radiation-balanced gain of 20 dB: it amplified an 800-μW signal to 84.2 mW with 433 mW of input pump power. The significance of this result is underscored by the small diameter of the single-mode fiber core (7.8 μm), which makes cooling more challenging. This study further demonstrates the viability of achieving substantial gain and energy extraction in a small-core Yb-doped silica fiber while effectively utilizing anti-Stokes fluorescence to keep it cool.