Coolant temprature should not vary much unless you are stalled or moving at very little speed. If you have your fan working properly, it should maintain safe operating temprature for engine. On most gauages, midway point is normal.
Please head some warning. If you engine is too hot, but your fan is working, you should let the car idle before turning off engine( couple of minutes). this allows for coolant to keep in circulation for a while and helps cool down engine before engine is stopped. Also should not add cold water right away, as it will change metal temprature upon contact. Do not put cold water on the engine. Metals exapand and shrink due ot temprature, may loosen some seals or contact points. Once car is coll down( 15-20 minutes, carfully open coolant reservoir and add additional fluids to reservoir. Opening radiator cap( if your car has one) may release steam and cause burns.
Finally if you need additional fluids, then have your coolant system check for coolant water mix or leaks. Coolant chemicals help increase boiling point of the water to a higher temperature. This helps keep coolant water mix in fluid form and avoid steaming or increased pressure in coolant system. Mot cars heat up due to less than optimal mix of coolant-water in your vehicle or leakage, or fan issues. Never add tap/stream water to engine. I recommend adding distilled water and coolant mix according to manufacturer's recommendations. Tap or stream water has salts, that will sit in your coolant system, usually causes long term issues, most common is thermostat or temperature sensor failures. Also if you have not used life time coolant, then make sure you change your coolant regularly based on coolant life. Old coolant changes PH, and causes engine corrosion.
I hope this helps.