Most soft box companies, Photoflex, Chimera etc all make products for the movie and TV industry. Their softboxes are designed to take the heat. Where you will run into to trouble is adapting the light to the softbox.
These companies make "speedrings" which fit on most lightheads that are designed for photgraphers, still and video etc. These speedrings attach easily to the the light head and then to the softbox.
In your application you would have to adapt some sort of universal "speedring" to those lights and it may or may not be easy.
If you shoot black and white it shouldn't matter too much about the color temp. In color you would have to, as others have mentioned, filter either the lights or the lens.
For more info on softboxes just do a google search or Photoflex or Chimera.