Firefox Portable leaves files on host?

I started to use Portable Firefox and Thundbird under the assumption that they do not leave ane traces on the host I use. In contratry to this assumption Firefox definitely writes filesonto the hard disk of the computer of the network of my employer and leaves them even after removig the USB-stick. Can I do anything against this? These files grow so big sometimes that I am prompted to wipe them off before logging out from my account under XP.
Regards
Franz47