As temp in cars in the sun can reach 100C/212F under the worse scenarios (75C/167F under "normal"), which is a bad temp for
batteries, I will go against all those that say to leave it in car, I still say that leaving it is a bad thing.
The "using a small cooler things"... at these temp. unless it's a powered one with external vents for heat exchange, those things would only "work" for a couple of minutes more... plus between having to drag icepacks, etc. that would be involved...and wouldn't work for much time unless you get a very well insulated one..
I stick to the get something to carry it with you advise.
Switch from pocket-less shorts to jean shorts, or other that have pockets... if you have a wife/girlfriend, have her put it in her purse (upright to prevent leakage if possible).