Oh c'mon, this isn't even close to Walters territory.
I'd recommend getting rid of the blanket and amp case (whatever that is!). I think that you're just asking for something to overheat, especially if you're doing this for long periods of time. If you're doing that for volume control purposes, I don't think that you need to really crank one of those Cube amps to get it to sound good. So just turn it down and ditch the blanket/case. I know that turning it up loud enough to involve the speaker in the whole equation is a good thing. But your Cube may sound pretty close to the same at a lower volume.i
Mixsit has a good suggestion. You might even try experimenting with mic placement. The closer the mic is to the center of the speaker cone, the less bass it'll pick up. The closer it is to the perimiter of the speaker, the more bass it'll pick up (relative to other frequencies, that is).