Hi, from what you describe so far, I would be considering the thermostat or the water pump impeller.
If the thermostat is failing to open when hot, this would prevent the water from circulating and cooling the engine.
You can test the thermostat by removing it, boiling a pan of water, then placing the thermostat in to see if it opens, if it does, I would then consider repeating the test but using a thermometer to heat the water slowly and observe what temperature the thermostat opens at, usually it is around 87.5 degrees Celsius. Often though it is cheaper and easier to just replace it and see if it makes any difference.
If it isn't the thermostat, the next most common issue is for the impeller that circulates the water to be slipping on the shaft of the water pump and therefore not circulating the water.
The last most common cause is cylinder head gasket failure, although I expect this to be unlikely on your description so far, most good workshops would be able to do a sniff test if there are any suspicions of the coolant looking for by-products of combustion in the coolant being given off when warm and a compression test if deemed necessary.
Let me know if you need anything further.