I have had them fail both ways, most recently the freelander stat failed open followed by the RR doing the same. That said my VWs have never failed that way.
I've had two fail 'by' over cooling one on a P38 and one on a 90; didn't work out why they failed but opening far more than they should at a give temperature was the problem, fixed by a new 'stat in both cases (with the same temp spec)
