I'd imagine its down to the fast idle when cold. If you hold the warm car at the fast idle revs (around 1k RPM I think) then you should be able to reproduce it. TBH it depends on whats causing it, but something obviously isnt tight enough (perhaps a joint somewhere) or its too close to a cross member or other part of the body. Either way having it up on the ramps they should be able to sort it. I cant see that the engine would move more when cold but perhaps it does, I'd imagine its down to the higher revs at cold idle or one of the joints when it warms up.
Remember also that the y-pipe doesnt have a flexi pipe so any movement will be transmitted all the way back to the tips, so even the smallest movement I guess could cause contact somewhere.
And yes 8:30am is too early. Would have come if it were just me, but the missus wouldnt appreciate leaving that early!