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 $∼ 10^{-11}$ \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 Å and in the \ion{C}{2} multiplet at 1335 Å. We find no wind absorption in the \ion{C}{4} 1550 Å doublet observed at the same time as the \ion{C}{2} 1335 Å line or in observations of \ion{O}{6} observed simultaneously with the \ion{C}{2} 1037 Å 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. ; Comment: 17 pages, 3 figures, Figure 1 in 2nd version fixes a small velocity scaling error and new revision adds a reference to an additional paper recently found