Excessively high engine temperatures can cause engine knock, which speeds wear on virtually all key engine parts, including pistons, pins, crankshaft and bearings. High temperatures also thin the engine oil, increasing friction , engine wear, and causing parts to warp, which affects engine sealing, which inturn reduces power.
You should regularly re-fill the cooling system. Many late-model cooling systems can trap air, which reduces heater output and can create harmful hot spots in the engine. If the car manufacturer has a specific bleeding procedure, which would include the opening of air bleeder valves on the engine block or cylinder head, be sure to follow it when filling your radiator. If the radiator cap is not the highest point of the cooling system, jack up the front of the car and raise it (or park your car so the radiator cap is on the highest point on the slope), which helps it self-bleed. Make sure the reservoir is filled to the proper marked level, and recheck the level periodically.
Check the clutch fan on a north-south engine, and in particular, measure the air temperature when the clutch locks up. Use a pyrometer (basically a heat gauge that can measure much hotter than the run-of-the-mill thermometer) on the fan shroud and run the engine until it warms up. When the engine is warm, the fan should lock up, fan noise will increase, and the temperature should be between 150° and 170°F.
If you don't have a pyrometer, try to spin the fan after the engine is warmed up (but turned off). If the fan turns easily, the clutch is bad. Also, if you run a finger around the bearing area at the rear of the clutch assembly and it picks up a blob of goo, it's likely silicone from a leak from the clutch assembly. It is not a difficult project to unbolt the clutch fan assembly and install a replacement.
Test the radiator electric fan, or fans. About a minute after turning on the air conditioner, at least one fan should turn. Refer to the Owner's Manual to see if/when a second fan turns on or the single fan switches to its high-speed range. You may have to block the front of the radiator or a/c condenser with cardboard to raise coolant temperatures high enough to fully check a multi-speed fan system.
Check that the fan shroud is not missing, which would reduce the efficiency to the fan. A missing thermostat can prevent proper engine warm-up, especially on cold days. If the car's computer thinks the engine has not warmed up, it continues to run in overly rich warm-up mode, which is less fuel-efficient, and will not circulate coolant to the engine.
Look under the front of the car. Many modern cars draw in cooling air from the underneath, especially if the design has a limited grille area. A missing air dam or chin spoiler may cause the car to run hot, especially on highways.