See if you can get hold of a good guy for radiator, get it full serviced, keep your eye on any rust like deposit in radiator (can notice rusty color when you open the cap of it) the rubber/silicon pipe coming out of radiator top side goes into a metal pipe, that piece of metal pipe can be disassembled for replacement or inspection. You can ask you guy to take it out for you and inspect if it is rusty on the inside, if it is -- that's one issue of your car heat up. Previous owner(s) were running car with tap water in its radiator -- which is like a poison to a car's cooling system.
For a full service of your cooling system or just radiator, ask your guy to make use of mild acidic solution (water with a bit of tartari (tartaric acid) will be good enough) so to get rid of rust as much as possible.
white smoke is a sign of concern, seems like you car overheated well enough -- was that white smoke misty? that can represent a leak in cooling system which may have blown out steam from some point. Water/Coolant in cooling system works under pressure and it would lose its pressure if the system is leaking from any point, sucking in air and dropping its efficiency (in cooling the engine).
This is my temperature reading with a full AC and stopped at a signal at 2:00PM (ignore the gear light, didn't get time to replace the tiny bulb behind D )
Note that, I'm running on Toyota's coolant with with a thermostat valve and auto fan.
but yes, also check if your engine oil is still an "oil" .. overheating can lead to damaged head gasket (if that gasket is very desi, because good quality gaskets can bear some heat). A damaged gasket creates a mess inside engine block and you get a creamy paste (mix of oil and hot water) running in your engine.
in that case, it needs clean up with complete oil change, oil filter change and a new head gasket.