High power continuous-wave (CW) single-frequency 1342 nm lasers are of interest for fundamental research, particularly, for laser cooling of lithium atoms. Using the popular Nd:YVO4 laser crystal requires careful heat management, because strong thermal effects in the gain medium are the most severe limitations of output power. Here, we present a multi-segmented Nd:YVO4 crystal design that consists of three segments with successive doping concentrations, optimized using a theoretical model. In order to quantify the optimization, we measured the thermal lens power of conventional crystal designs and compare them to our multi-segmented design. The optimized design displays a two times lower thermal lens dioptric power for the same amount of absorbed pump power in the non-lasing case. Using the optimized design, we demonstrate a high power all-solid-state laser emitting 10.0 W single-frequency radiation at 1342 nm when operating the laser crystal at room temperature. Further integration of the laser allows us to operate the laser crystal below room temperature for improving output power up to 11.4 W at 8°C. This is explained by the reduction of energy-transfer upconversion and excited-state absorption effects. Stable free-running operation at the low temperature of 8 °C is achieved with the power stability of ± 0.42 % by peak-to-peak fluctuation and frequency peak-to-peak fluctuation of ± 72 MHz in three hours.