the only proper way i know to cool down a hot barrel on a rifle is time.
my general rule of thumb on barrel temperature, is if i can't grab ahold of the barrel and hold it, then it's too hot and needs to cool down.
i generally shoot five shot strings, then let the rifle cool down about 5-10 minutes, depending on outside ambient temperature. on a really hot summer day, about 95-100 degrees, i may even go longer between shot strings.
as general rule, sporter barrels can be every bit as accurate as a heavy varmint barrel, but they will heat up much quicker and possibly throw accuracy off. heavy barrels, can usually go more shots before heating up and accuracy degrades.