That's exactly the same symptoms I have on an 2005 A3. I had it diagnosed as Dual mass flywheel, it sounds like a brick in a washing machine when cold but not there under load or if you depress the clutch. Been like it for ages, its on my list of things to do but still drives fine for now, I don't have any gear change issues...yet. I know it won't get better but I'm in denial, plus it will be a good excuse to drive the V5 when it goes.