Shooting long strings in short periods of time will not only affect accuracy, but will erode your throat and shorten the life of your barrel.
Every rifle is different, depending on the metallurgy and cartridge the rifle is chambered to. When shooting, if your barrel is getting too warm to the touch, imagine what it is doing to the inside of the barrel.
How much is your group opening up with over the string of shots, compared to your normal, slow fired group of 10?
Or is it the result of being rushed to take those 10 shots affecting your trigger control and shooting form?
As your barrel warms and expands, have you checked the floating of the barrel to see if it is starting to come into contact with the stock? Can you still run a sheet of paper down between the stock and the barrel?
Shooting it and giving it 2-3 minutes between shots keeps the temps down and will prolong its life (and accuracy).
Just some thoughts to ponder...
If you are wanting to spend more time shooting during these sessions at your club, you may want to use a different rifle for this, and use your Tikka in 308 for regular practice/shooting/hunting at different times.
For long shot string session, you may want to consider a milder load for your rifle, or a milder cartridge in a rifle with a heavier barrel, or even a carbon fibre barrel that dissipates heat more quickly than steel.
If you are thinking that you like your Tikka and want the feeling to be the same as your regular rifle, than look at another Tikka with a varmint barrel, mounted with the same scope as your 308, so that your trigger, safety and sight picture are going to be the same,regardless of which rifle you are shooting. This breeds familiarity, comfort and confidence!