Ok, one more time. You do not have a cat in that box. Look at the fiche at bike bandit. For the Standard/Classic models the catalyst box lists for $640 and has two outlets on one side, for the two mufflers on that side. The Touring model for 2008 was the only one with a single exhaust on each side, thus the parts are not interchangeable.
The box serves to equalize pressure between the two sides, necessary due to the different lengths. It may run a bit hotter, but you'll see no real difference in performance without it. If you had a set of Triumph mufflers without cats, they were TORS. If you aren't running a proper tune for your exhaust the header and exhaust temps will be higher because you're likely running too lean.
If you're looking for a performance boost, get a set of Jardines.