15 to 30 seconds. Even for a 30-shot string; no accuracy problems.
I have a sporter weight barrel and will shoot a 3-5 group in that amount of time also, I have shot many groups under 1" at 100yards doing that.
Barrel doesn't even heat up that much, well not that I'd really know but it just feels warm in my hand and it still groups fine.
If I had to wait 5 minutes between shots I'd give up, the weather here would've changed from sunny to snowing in that amount of time (a slight bit of exaggeration).