I just had to shoot a computer monitors for inserts in a PBS documentary.
For starters I used 5600K (in may case really 5200K) lights to make everything else more blue to lessen the difference. If you only have tungsten lights, use CTB gels. Then I went into the menu on the monitor and tried the color temp choices to further close the color gap.
A note on color temp momenclature here -- HIGHER color temps yield a bluer picture, which everyone "wrongly" calls COOLER. Conversly, LOWER color temps yield a more orange picture which everyone "wrongly" calls WARMER. Simply put, color temp is very counter-intuitive, and the "incorrect" usages are so endemic that they are "correct."
Anyway, you probably want the numerically lowest color temp (xxxxK) the monitor has, perhaps 3200K. If that hasn't removed enough blue, there may be a "user" or custom color temp setting that will allow you to change each color separately. If so, dial down blue, bring up the red, tweak the green, etc. In short, make it look right TO THE CAMERA which will not necessarily look right to your eye. You might find it useful to display white on the screen while you do this.
In addition to these valuable color temperature tips, I would also do the following:
Light up the set. Put color bars into the plasma screen and shoot it second camera known to be right... hopefully it'll be the camera you'll use during the show. Shoot the plasma screen TIGHTLY, filling the picture with the bars. Looking at a vectorscope and waveform monitor, misadjust the plasma screen until the bars look darned close to what they should be on the scopes.
Once that's done, run a test with talent and pictures in the plasma screen. Tweak to taste, but make sure the video in the plasma screen is set up right, or you will be doing yourself no favors at this point.
Argue with the physics people. The higher the temp the more of the shorter wavelenths ae present and the shorter wave lengths have ALWAYS been referenced as being cool as the shorter eave lengths which produce the orange light are referenced as warm. Unless someone starts rewriting physics text books I am not sure how you can refer to these terms as wrong. They are the proper way the entire lighting AND science world reference light.
The easiest solution is to check if the plasma screen has RGB gain controls which in effect will change the color temp of the monitor. You can change from 6500K to 3200K to match your foreground lighting if you are using tungsen.
Another solution which I use all the time is to use a primary (allows gain,black,and gamma RGB correctinl. Put the color corrector between the playback source and plasma screen thereby allowing color correcting the image to 3200K. This allow a real time method to get the best color and brightness reproduction of the playback sources on camera.
You could rent the following color correctors Sony BVW-10 (component inputs with composite and component outputs) or FORA composite color corrector -(composite in and out). Call any major video rental house to see what they have available.
Hire a qualified video controller to shade your camera and run the color corrector and you will be fine.