  It has recently been suggested that the winds from Classical T Tauri stars in
general, and the wind from TW Hya in particular, reaches temperatures of at
least 300,000 K while maintaing a mass loss rate of $\sim 10^{-11}$ \Msol
yr$^{-1}$ or larger. If confirmed, this would place strong new requirements on
wind launching and heating models. We therefore re-examine spectra from the
Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope and
spectra from the Far Ultraviolet Spectroscopic Explorer satellite in an effort
to better constrain the maximum temperature in the wind of TW Hya. We find
clear evidence for a wind in the \ion{C}{2} doublet at 1037 \AA and in the
\ion{C}{2} multiplet at 1335 \AA. We find no wind absorption in the \ion{C}{4}
1550 \AA doublet observed at the same time as the \ion{C}{2} 1335 \AA line or
in observations of \ion{O}{6} observed simultaneously with the \ion{C}{2} 1037
\AA line. The presence or absence of \ion{C}{3} wind absorption is ambiguous.
The clear lack of a wind in the \ion{C}{4} line argues that the wind from TW
Hya does not reach the 100,000 K characteristic formation temperature of this
line. We therefore argue that the available evidence suggests that the wind
from TW Hya, and probably all classical T Tauri stars, reaches a maximum
temperature in the range of 10,000 -- 30,000 K.
