In this picture, the f4t5 lamp is living the last moments of it's life. It was a cool white lamp, but something interesting I observed is that the color temperature got warmer as the lamp died.  It didn't change much, but went from 4200k to about 3500k. Why is this?

Interesting effect. Normally, the lamp will shift to a bluer color due to higher Mercury vapor pressure. Unless the thing here was the glow from the ends tricking you, or extreme phosphor decay.