2000 Volvo V40 Temperature gauge idling high

The gauge is indicating an overheating condition. Does it come down at highway speeds or when you turn the heater fan on "high"? Has the reservoir remained full or have you been adding coolant?

Higher road speed draws more air through the radiator. A higher heater fan speed draws more air through the heater core which is a small radiator. Both of those actions remove heat from the coolant. When that lowers engine temperature, it suggests the radiator isn't giving up enough heat on its own. Most commonly that's caused by an inoperative radiator fan. It is needed mainly at low speeds when there isn't much natural air flow.

If the fan is working, check the radiator for debris blocking it first, then look at the cooling fins to see if they're corroded away. Normally corroded fins will cause overheating at all speeds but running the heater fan on high will still help to cool the engine.

The coolant temperature sensor tells the Engine Computer what the temperature is, then the computer turns the fan on when necessary. Other than that, sensors don't cause overheating or other things to happen. They only report what has already happened.

Coolant doesn't circulate through the reservoir like it does in the radiator. All you should see is the coolant level goes up when the engine is hot, and it goes back down when the engine cools down over about an hour or two. You'll see a "hot" and a "cold" mark on the side of the reservoir As long as the level stays between those two points, it's okay.