It was probably passing a few packets between the powerline network ports it feeds and the router, but there were no computers connected or active.
It certainly doesn't seem hot to the touch at the moment and it wasn't warm when I pushed over a TB through it from one local computer to another (although since this was between only two ports, it probably wasn't very taxing).
My only issue with contacting D-link is that the switch will definitely be out of warranty, but I'll give them a try at some point when I get a chance to sit down and call them.
I think this has now fallen into the 'annoying that I can't solve but not really causing too much aggravation' pile.