A heavier barrel will not dissipate heat (get rid of heat) faster than a lighter barrel. A heavier barrel will heat up and coll down slower than a lighter barrel. The lighter barrel will heat up and cool down quicker.
I can't weigh in on how long a string you can shoot before your groups start opening up with varmint vs bull contours. There's usually a bigger difference between sporter and varmint then between varmint and bull.
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