We present 50 individual measurements of the gas temperature and turbulent velocity in the local interstellar medium (LISM) within 100 pc. By comparing the absorption line widths of many ions with different atomic masses, we can satisfactorily discriminate between the two dominant broadening mechanisms, thermal broadening, and macroscopic nonthermal, or turbulent, broadening. We find that the successful use of this technique requires a measurement of a light ion, such as DI, and an ion at least as heavy as MgII. However, observations of more lines provides an important consistency check and can also improve the precision and accuracy of the measurement. The weighted mean gas temperature in the LISM warm clouds is 6680 K and the dispersion about the mean is 1490 K. The weighted mean turbulent velocity is 2.24 km s^-1 and the dispersion about the mean is 1.03 km s^-1. The ratio of the mean thermal pressure to the mean turbulent pressure is P_T/P_xi ~ 26. Turbulent pressure in LISM clouds cannot explain the difference in the apparent pressure imbalance between warm LISM clouds and the surrounding hot gas of the Local Bubble. Pressure equilibrium among the warm clouds may be the source of a moderately negative correlation between temperature and turbulent velocity in these clouds. However, significant variations in temperature and turbulent velocity are observed. The turbulent motions in the warm partially ionized clouds of the LISM are definitely subsonic, and the weighted mean turbulent Mach number for clouds in the LISM is 0.19 with a dispersion of 0.11. (Abridged)
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