I see also a well established 800 year cycle here. My own efforts suggested as much with less precision which may not exist either. There is a climate cycle and it may have such a period. It is likely driven by the circumpolar current which likely accommodates a massive exchange between the Pacific and the Atlantic.
Yet the contribution may also be one degree or less but sufficient to exaggerate local effects of volcanoes. We simply do not know but we do know that human CO2 contribution is laughable compared to out volcanoes.