There really isn't much you could do outside of insulating your case. I wouldn't wrap the pump in anything because it will overheat. Try permanantly pounting it to your case with foam in between. That will at least hold the pump firmly in place.
not sure about yours, but when I first got my pump it was extremely noisey... poor design I suppose but the impeller actually rubbed against the plastic causing it to vibrate and be off blance causing more noise. I was able to slide the impeller a little so as to space it away from the pump and then superglued it to the drive rod to keep it in place. Perhaps a similar fix would work for you.
Hi folks, I have a little more time to work on it today some more.
It seems like my pump make even more noise now. The vibration translate to the copper tube at the side and vibrate the whole case. I have to extend the tubing a little more.
This pic link down here is my rad (toward the middle) . It does not work very well at high ambient. But it work well in the winter
I think it could be transmitting along the vinyl tubing if the stuff is a bit stiff. If it is like pulsing the water flow, all elements of the system could be a source of hum though, that would be virtually impossible to get rid of.