On my (2) 850's and on current S70 all of the tstats have failed in the open position. I've not known one to fail in the closed position. With the tstat stuck open the motor is slow to warm and over cools when coasting down long hills. When I see the temperature guage reacting in this way I schedule the tstat replacement pretty soon after. I've not heard of any damage to car's systems by running in this overcooled condition, but I am aware that the fuel system tries to compensate for the cooler running engine by adding more/ritcher mix.

The tstat replacement is not all that expensive, even at the dealer.

good luck with this matter,
Clive
San Diego