Q: Need help on what is going on with my car heating up

I got an transmission and coolant flush not too long ago. A week later my car overheated for the first time since I owned it. Turns out they didn't put in enough coolant in, I did go back and they filled it completely. But the next day it started to heat up again. Please keep in mind that these days had been exceptionally hot and every time it did start to heat up I always pulled over to let it cool down before driving. What I have noticed is that it only heats up on days that the sun is really hot and it takes a little bit of driving before it gets to a point where I need to pull over. I really don't want to go to a mechanic until I have a good idea as to what I need to be fixed. Or is this just because my car is almost 13yrs old? No lights have turned on nor does it rise rapidly when it's idle. I am at a loss to what is wrong with my car. Please point me in the right direction!

My car has 120000 miles.
My car has an automatic transmission.