Moberg et al.  use the July temperature reconstruction of Korhola et al.  using Lake Tsoulbmajavri diatoms as one of 11 low-frequency proxies, as shown in Figure 4 of Korohla et al. reproduced below. There is obviously nothing in this reconstruction that is inconsistent with a pre-hockey stick view of climate history.
. (Original) FIG. 4. Reconstructed mean July temperatures at Lake Tsuolbmajavri for the last 10,000 years
Korhola et al. note the very strong warmth (~7000-5000BP) in the Holocene Optimum , which they associate with the maximum distribution of Scots pine in northern Fennoscandia reported elsewhere between ~6500 and 4500 BP, when the "altitudinal pine limit reached up to 200 m above the present limit", contemporary with a similar expansion on the Kola Peninsula, Russia.
They associate the maximal temperatures at the end of the warm period from 2400-900 BP with the Medieval Warm Period (about AD900 to 1300) [Lamb, 1995], noting comparable effects elsewhere:
two boreholes on the Greenland Ice Sheet (Dahl-Jensen et al., 1998) and in records from lakes (Stager et al., 1997; Rietti-Shati et al., 1998) and mires (Street-Perrott and Perrot, 1990) in Africa; it is also seen by glacier recession in different parts of the world, including Swedish Lapland (Denton and Karlen, 1973)
They associate the subsequent cooling phase with the Little Ice Age (about AD1550-1850) [Grove, 1998], noting that:
There is an increasing amount of evidence to document that subarctic and arctic lake ecosystems experienced marked changes in their limnology during the LIA event (Douglas et al., 1994; Anderson et al., 1996; Sorvari and Korhola, 1998; Korhola et al., 2000b).
The relationship between MWP and 20th century levels in this proxy is obviously different than in the Moberg proxy-only reconstruction shown here. I’m continuing the examination of Moberg et al  low-frequency proxies to clarify their individual contribution to the overall low-frequency reconstruction.
Reference: Korhola, A., Weckstràƒ, J., Holmstràƒ, L. & Eràƒ⣳tàƒ P. A quantitative Holocene climatic record from diatoms in northern Fennoscandia. Quat. Res. 54, 284-294 (2000).