Cz:
Just make sure that you only use Portable Firefox and ONLY THAT - remember if you display something like word documents, pdf files, nudie PICTURES, VIDEOS, which open another program installed in the laptop eg. Windows Media Player, that would leave traces in your laptop.
I am also not sure how the Adobe Flash player behaves in Portable Firefox eg. where the cache is or if you can change the cache location etc. Therefore, even watching XVideo or YouPorn may potentially leave traces. I know you can install Flash player directly onto Portable FF, but I cannot guarantee your browser does not use the copy of Flash player already installed on your laptop.
The only sure things which are potentially safe are text and pictures (displayed in your browser).
The more I think about it, the more I worry about it!!!
An ultimate solution is to boot and run an alternative Operating System (OS) eg. a version of Linux such as Knoppix from a USB drive. This will completely bypass the native OS on the laptop. Usually these portable OS already have browsers, video players, picture viewers and OpenOffice for use. They use the RAM or the free space on the USB stick for cache, and it does not use the hard drive of the laptop at all.
However this is quite a hassle, and performance is going to suffer a lot (system response will be limited by the speed of your USB stick, not the CPU not the amount of RAM etc.)
The more I think about it, the better to use your own smartphone (3G or wifi)!! It is probably a safer bet and more convenient!!!