Hi GSP,
I also experienced similar accuracy problems with my Sako 85 (.308 hunter, laminate stainless) - the groups looked similar to yours, including the rise in shot placement when hot. It's seriously frustrating when you've dropped £1.5K on a new rifle. I have a S&B 8x56 sitting on Optilock rings and bases, given their good reputation I ruled that out to start. I also got no test fire card (apparently they don't provide them anymore). only a 'Certificate of Accuracy' guarantee or some other such toilet paper.
Here's what I went through to make things better.
When I first got it (new), I wouldn't group within about 10". After trying 4 types of factory, 123gn Sako, 150gn Winchester PP, 150gn Hornady American Whitetail and 150gn PPU, it turned out to be the a faulty sound moderator (forget which make) which wasn't cut right, so the thread didn't meet the crown properly. A strip down clean of the moderator revealed the first baffle was being 'clipped'. Needless to say I wasn't impressed (safety). Moderator off, the groups immediately reduced to about 1-1.5" @ 100m with the 150gn Winchester PP and the Hornady. Funnily enough, the 123gn Sako Hammerhead wouldn't shoot anywhere near as good. Swapped sound moderator for a Tier One Spartan (nice bit of kit but a bit loud) and the rifle held 1-1.5" groups, although I still wasn't happy given the 0.5MOA claim. Of course you should be able to rule out the moderator from the middle group in your picture, everything's consistent whether on of off.
In a (probably unnecessary for a stalking rifle) quest to get better groups, I looked at other things starting with phoning Riflecraft who said it should shoot better, but didn't think it would be the rifle in their experience. When it was new I followed a 'running in' procedure for the barrel of one shot, clean, 2 shots clean etc etc. On their recommendation I bought some of the Boretech Eliminator cleaning fluid from Riflecraft and thorough cleaned the rifle. Good stuff, it doesn't stink and cause wife complaints and you wouldn't believe the crud that came out on the patches, even after many passes of the patch. Just watch that you don't use brass/copper jags as the chemical creates blue/green staining from the copper.
A good cleaning improved the groups to around 1" consistently. I now routinely clean after either (i) 20 shots or (ii) a stalking trip. I also checked all the scope mounts for tightness, as well as the action screws on the bottom of the stock (they were a bit loose, so hand tightened them but perhaps should torque to the 5nm that someone else mentioned?
I've been happy with the rifle ever since, and am sticking to using 150gn Winchester PP or Federal Power/Vital Shok. It still won't shoot quite as well as my mate's Schultz and Larsen Victory in .270win, but that was 2.5x the price. Also, as someone else said, this isn't a heavy barrelled target rifle so I wouldn't expect match accuracy, but certainly 1" groups at 100yds.
To summarise I would do the following in this order:
1) Take off scope and bases, re-tighten and re-fit
2) Shoot 2x 5 shot groups with a short cooling period between shots and a longer one between groups to check if that helps
3) Regularly check your moderator is tight (especially if it is modular as they can come loose independently). Never leave the moderator on after shooting or in storage as it can corrode the crown and ruin the accuracy
4) Really thorough cleaning regime - I recommend some of the Boretech Eliminator (no shares in the company I promise)
5) Check the stock screws
6) Try to stick with whichever ammunition you find shoots best