If it overheats at idle it is almost certainly due to lack of air flow through the radiator - and the fan is directly to blame. When sitting still the only air flow is provided by the fan - once moving it is mostly provided by the air hitting the grille.

If the radiator coolant flow were restricted in any way (or the airflow in some physical way - like a newspaper blown into the grill) the overheating would be much, much worse when the car is working hard - going 70 mph on the highway. The engine is disposing of much greater amounts of heat under those situations, and produces very little at idle.

Although some cars can suffer from broken waterpump impellers (Some years of BMW's had plastic ones which eventually have a 100% failure rate!) I doubt that the solid metal one in a Volvo pump would ever go bad. In any case the symptoms would be similar to a blocked radiator - rapid overheating when driving, slow overheating when idling.

PS - Never mind - I re-read the original post and realized that the gauge goes up and stays up. Are you sure it is actually overheating? Could be a bad gauge. If it reads excessively high but never actually boils over then it could just be a bad gauge or sender. Or a bad thermostat regulating at a high tmep - though they usually just stick either open or closed.