Figure 1 presents the variations in the global air
temperature [www.cru.uea.ac.uk/cru/data/tempera
ture] and in the amount of carbon dioxide in the
Earth’s atmosphere [http://climate4you.com/Green
houseGasses.htm]
Ok so their reference for CO2 levels aka the keeling curve is a
website called climate4you!
Fig. 5. Comparison of the temperature reconstructions obtained using the geothermal method: (a) the relative average global sur
face temperature (the solid thick line with regard to one standard error) compared with the relative variations in the global air
temperature (the 5 year moving averages) obtained instrumentally; (b) the surface temperature over Australia (1) compared with
the temperature reconstructed over the Northern Hemisphere (2) [Pollack et al., 2006] with regard to uncertainties.
And here is me thinking its only bad people who tap an instrument record onto a dataset.

Here is there global borehole reconstruction. 1500 is not the medieval.

Here is their borehole reconstruction that does hit the medieval and it is only from the Urals.
Fig. 4. The comparison of changes (a) in the GCR intensity (10Be and Δ14C): the radiocarbon concentration in the Earth’s atmo
sphere under the action of GCRs [Stuiver and Quay, 1980] (1), the GCR intensity based on the measurements of the 10Be con
centration in Greenland [Usoskin et al., 2002] (2), Antarctic [Raisbeck et al., 2002] (3) ice; (b) in the reconstructed temperatures
of the Northern Hemisphere: the smoothed instrumental series of data (1), the series of [Mann et al., 1999] (2), and [Moberg et
al., 2005] indirect data (3); and (c) in the data of borehole thermometry in the Ural boreholes [Demezhko and Golovanova, 2007]
during the last millennium: the minimal estimate (1) ± the double standard error relative to the average value, the maximal esti
mate (2), and the optimal estimate (3).
Taping a global instrument record onto an icecore! Wow.
They are also proposing a -1.5C temperature change for the little ice age? That kind of change would push us to the brink of a return to glaciation. If the earth is that vulnerable to changes in solar output then why is it suddenly completely invulnerable to changes in the greenhouse effect? But that said I really strongly dispute their 1.5C figure as having any global meaning.
These two papers are largely a lot of editorialising about how the bog standard tropes of the skeptics and very thin on anything new. If anything they are getting referenced as a "peer reviewed" source for the usual Watt\ Morano\ Monckton type talking points.
The actual borehole data is a little well, interesting. Certainly would have been a very short paper if they had stuck to talking about boreholes. It shows a figure of the little ice age that if taken serisouly means we have a very very sensitive climate. But it is a very poor fit for past solar activity which shows a lot more variation than their reconstruction is showing.
On the whole I am not really seeing why anyone who had actually read the paper would want to use it. Unless the intention was to use it as a reference and hope no one else would read it.