We have a 95 855 (70K) and 98 S70 (60K). I've had to top off
coolant in each of them after a couple of years. In my case,
the light came on for a second when you accelerate (since
that makes the fluid move in the bottle triggering the sensor).
Eventually it would stay on. I do not have any coolant leak --
I'm not sure where it goes.

The sensor that reads the fluid level has been known to fail.
If the fluid level is correct, and the temperature gauge
reads OK then I think it might be the sensor. I don't think
you need a fluid flush (Volvo service never even calls for it).
It won't hurt but probably won't fix the problem (unless it
really is low fluid level in which case topping up would do it).
I'd also leave the thermostat alone since the temperature is OK.

Just in case it is low fluid level, you could add just a bit
of distilled water (when the engine is cold) to bring the level
up a bit. Couple of cups would do it. If you add coolant I would
only add Volvo coolant (about $17 a gallon at the dealer). Do
that and then see if the light goes out. If not, probably the
sensor in the resevoir is having problems.