We report the determination of free-electron concentration and mobility of free-standing GaN nanowires (NWs) by line shape analysis of the coupled longitudinal optical phonon-plasmon Raman modes (L+). The E2high phonon mode at 566.9 cm-1 with a sharp linewidth of 2.8 cm-1 indicates strain free NWs with high crystalline perfection. The lattice temperature of the NWs was varied between 313 and 472 K by varying the excitation laser beam power. For unintentionally doped samples at room temperature, an average electron concentration and mobility of strain free NWs were found to be ∼2×1017 cm-3 and 460 cm2/V s, respectively. We have shown that the electron concentration does not change significantly over a temperature range between 313 and 472 K. The electron mobility decreases at high temperatures, in agreement with literature data for compact layers. For Si-doped NWs, the L+ phonon peak is strongly upshifted indicating a higher free-carrier concentration of about 1×1018 cm-3. Asymmetric broadening observed at the lower frequency side of the L+ phonon peak might be ascribed to the enhancement in surface optical modes due to the high surface-to-volume ratio of NWs.