"The paper says that there is a change in temperature during the LIA."
" However it is quite clear that this reduction of temperature is due to a change in ocean currents (as discussed above)."
You keep stating this as if it refuted the temperature measurement itself. It doesnt. The same questioning of causes can be asked of every temperature sample. It does point out that a local measurement may be only relevent locally, and may no necessarily reflect global trends, to which I agree.
Now, I've given a number of sources, including the NOAA website, that state and confirm that LIA was a real and persistent global climate anomaly. If you don't think something that well-measured even existed, we'll have to simply disagree.
You must not understand my comments. I do not doubt that the cooling takes place. I say that "However it is quite clear that this reduction of temperature is due to a change in ocean currents". So I don't dispute the cooling, but I am questioning the cause. I think we actually agree on this point.
Also, I am very happy to accept that the MWP and LIA did exist. I don't know of anyone who says otherwise. What I object to is poor scientific methodology and biased reporting being introduced into the debate.
I agree, you have presented a number of papers. However I believe I have discussed most (all?) of them and have shown that they do not support the conclusions as presented.