  The heating and acceleration of the solar wind remains one of the fundamental
unsolved problems in heliophysics. It is usually observed that the proton
temperature $T_i$ is highly correlated with the solar wind speed $V_{SW}$,
while the electron temperature $T_e$ shows anti-correlation or no clear
correlation with the solar wind speed. Here we inspect both Parker Solar Probe
(PSP) and WIND data and compare the observations with simulation results. PSP
observations below 30 solar radii clearly show a positive correlation between
proton temperature and wind speed and a negative correlation between electron
temperature and wind speed. One year (2019) of WIND data confirm that proton
temperature is positively correlated with solar wind speed, but the electron
temperature increases with the solar wind speed for slow wind while it
decreases with the solar wind speed for fast wind. Using a one-dimensional
Alfv\'en-wave-driven solar wind model with different proton and electron
temperatures, we for the first time find that if most of the dissipated
Alfv\'en wave energy heats the ions instead of electrons, a positive
$T_i-V_{SW}$ correlation and a negative $T_e-V_{SW}$ correlation arise
naturally. If the electrons gain a small but finite portion of the dissipated
wave energy, the $T_e-V_{SW}$ correlation evolves with radial distance to the
Sun such that the negative correlation gradually turns positive. The model
results show that Alfv\'en waves are one of the possible explanations of the
observed evolution of proton and electron temperatures in the solar wind.
