Sounds like water pump may be on its way out, impellers can corrode away, or become detached from the shaft, losing efficiency at higher engine running speeds, a new thermostat may be a good idea too... flushing the system is a good place to start though, drain system down, and flush as much out as possible with a hose to get the worst out.... then add a mug full of washing powder slowly to the system, Persil works wonders... let it run in the system for half an hour or so, drain, re flush and replace with just water, take the car for a drive to test, if OK, drain some water out, and top up with antifreeze
Thom