First check the coolant level yourself while the engine is cool. Remove the coolant cap at the front passenger side of engine. If your coolant is low enough, topping off the reservoir doesn't do anything for you.
Start the car. Turn on your AC if it works. The radiator fan should come on.
If not, you have a problem in that circuit. Run the car for awhile. The fan should come on by itself roughly 220 degrees F, not sure the exact amount, every manufacturer has their spec.
If it never comes on, you have a problem in that circuit. If it does, check airflow in front of the radiator. Bent air fins on the condenser can block air from flowing through the radiator.
Was the coolant bad before the rad/thermostat change? Sometimes rust buildup in the block can restrict a brand new radiator or heater core. When the engine is hot try to feel the hoses to the heater core.
Both should be hot. Sometimes bad head gaskets/warped cylinder heads can do this. They have a tool that you fill up with a blue liquid.
You squeeze the rubber bulb at the top to suck the coolant vapors into the tool. If combustion gases are present in the coolant, the blue fluid turns green.
First off, find a different "mechanic". Any mechanic who says it looks like it hasn't been flushed so it's easier to change the radiator just wants the extra money he charged you to change it. Do you keep a close eye on the level of coolant in both the radiator if equipt with a removeable cap when the engine is cool.
If you only get hotter when at highway speeds and the coolant is at the proper level, I would have the transmission checked out. It's the only thing that can put extra heat into the radiator while driving the highway.
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