This was a long time ago in a galaxy far, far away when I owned my K12S.
As such, I never kept the details. To be honest, his price was virtually the same as the BMW rad, his work was uknown to me, the finished rad may well have been too heavy for the relatively flimsy BM mountings and I would still have needed to buy a thermostat.
A google search will reveal any number of guys advertising bike rads and I just ploughed throuh them on the phone.
In the end I bought new. I had some discount from a neighbour who worked for BM but would still have bought new in the circumstances. You know it fits, you get a new thermostat and you get two years warranty. The guy oop north won't give you any of that.
My advice, along with all the other tight gits in here who have thought long and hard about 'wasting' their hard-earned dosh on an overpriced, badly designed and manufactured BMW item, is...
...get a new one. We all did, even though it hurt like hell.
As for the intermittent overheating. Possibly a failing thermostat but I've never heard of one. Don't bother asking either, it is specific to BMW and costs appropriately.
As an aside, and because you haven't introduced yourself so I don't know the history, does the bike have a full BMW service history? If someone other than BM have been at the plugs, coils or valve shims and not done a proper vacuum re-fill of the cooling system then you could be storing up more than a dead rad. You could have air pockets in the head which will lead to all manner of broken and cracked bits of expensive ironmongery.
Welcome to the madhouse that is EuroKClub and the world of BM ownership.