My S70 has been running poorly since I got here for work in northern North Dakota.
First the Thermostat works. When it is warmer the heater works great. The drive up from Colorado at night was okay the heater worked the temp gauge sat just above the2 major line from the bottom. Here for the last 2 days I can idle and get it above the mark. I drive and the temp drops almost to 0. The gas mileage has dropped through the roof. The car got great mileage driving here the night before this started now 89 miles is 1/4 tank.
The temps here with wind chill dropped to -16 and on the way home tonight the display showed -6F

 

How do you know that the thermostat works? The only real way to check it is remove it from the car, put it in a temp chamber or pot, watch where it opens when the temp is correct. Did you do that?

 

Change the thermostat. Just because your heater is working okay doesn't mean it's working right. Given that the problem is worse when it's colder outside, and that your mileage is getting bad, it sounds like the engine is overcooling. Many folks suggest changing the temp sensor at the same time because those do go bad as well, but I don't do that unless it needs it. Be careful when taking off the T- stat housing. The steel bolts tend to seize in the aluminum head and are a bit hard to turn. Use a high quality T-40 socket, not a cheap one or one of those L- handle things, and make sure the socket is fully seated in the hole and that you don't twist up when you turn it. Then, coat the bolts lightly with anti- seize lubricant- a small dab on the very bottom threads is enough, screwing it in will coat it.