Days ago our xc90 (2008 3.2L) auxiliary belt tensioner fails, then the belt stuck and it looks like the water pump was involved in overheat the engine. The engine became hot and the coolant deposit expelled the water. Also the power steering fails because it works in the same belt path.

The tensioner was replaced, belt and pulley also. But now the engine temperature gauge in weird. When the car is riding or accelerating the temperature goes down, then in idle or stop at lights, the temp goes up! (Not pass the middle) Of course when the car is moving goes down close to bottom indicator.

I was thinking about the thermostat but... could be a cracked or cut hose?

 

The water pump doesn't run off of the serpentine belt. It runs off of the timing belt. Maybe you should pull the t-belt cover and check it out in there. A bad water pump would mess with your engine temps I guess.
Or it could be a bad thermostat?

 

you can also check the connections to the coolant temp sensor - on the T-5s it plugs into the housing right below the thermostat. Most people replace the T-stat when doing the sensor so it may be a good time to do both. If the problem seems to be the gauge and your not boiling over, then that's the likely cause. But just the same, if you had a serpentine belt go, you sould inspect the timing belt as well to check for any collateral damage. Water pumps can start leaking through the bearing and will drip under the timing belt cover.