Some of you don't like to hear me repeat how things "used to be." However, all this talk about slow firing, to keep the barrel from heating up, etc, is from a new wave of shooters, who, for the most part, are shooters and not riflemen.
Most old time shooters with bolt action rifles, had their rifles bedded, so they could shoot five shots without the rifle walking the bullets.
Many of us used to shoot in competitions with our sporting rifles. Every competition had time limits, on how long you were alowed to get your five or ten shots off. Certainly, you were not allowed enough time to let the barrel cool during shooting!
Even bench rest shooters in sporting weight competitions are up against time limits.
Whenever I got a bolt action rifle, and I've had more than a few, the first task was to take them to the range and carefully fire five rounds, one after the other. If they made a nice group, without walking the bullets, happy days, we just sighted in. If they made a poor group, or walked the bullets, usually up, but could be any direction, we just quit firing, went home and took the rifle apart, to work on the bedding.
Over the years I have never had a bolt action rifle that I could not bed, so it would keep shooting to the same point of impact, as the barrel heated up.
Not all rifles are capable of consistant MOA groups, but none should walk the bullets as the barrel heats up. I had a very nice rifle,which I liked very much, but it would not group better than, maybe a bit under 2 inches, at a hundred yards. It obviously had a faulty barrel. I long ago sold the rifle, but I still have the remains of boxes of many different bullet types and notes on many different powders tried in it, but to no avail.
In the mid 1960s I purchased the finest rifle I maybe ever had. I bought a L61 Sako Finnbear in 270. The first time I took it to the range I litterally prayed that it would not walk the bullets. No luck. After three they started to go up and off to the side. It took me about three times of bedding and shooting, before I got it right. But, it was with a great deal of satisfaction that I finally could make a sub one inch, five group at a 100 yards, with the barrel too hot to hold onto.
I doubt if I have changed anyones opinion on all of this, so just carry on, let your rifle barrel cool and eventually put three shots into a good group.
But I shudder to think how you would make out if you were in a real life shooting competition with such a rifle!
Edited to say I just now noticed that the original post was about a lever rifle. So, sorry for all this about a bolt action, on your posting. Didn't mean to hijack it, just failed to read your post correctly.