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I have only seen the data on a couple of models used to reproduce previous temperatures, they were so-so.
On a computer that is unfortunately dead now I had built a rather basic model that went back 1000 years. I used the past data to fine tune the model as much as I could so the hind cast was actually fairly accurate. I didn't future cast because whenever I added CO2 to it things blew up in the modern day so I left it out and figured the discrepancy would likely be due to us. It showed approximately half of the observed warming was natural, and followed with the pause that used to be in the data-sets which was due to the long low portion of the solar cycle.
Mind you this was before the data-set changes a couple of years ago. If I was to do it with the way the data-sets are now it would show that we should be cooling (changed the TSI data as well). Meaning that we are responsible for more of the warming than has been observed.
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