In Intelligence Explosion analysis draft: introduction, Luke Muehlhauser and Anna Salamon wrote

Svante Arrhenius' (1896) models of climate change lacked modern climate theory and data but, by making reasonable extrapolations from what was known of physics, still managed to predict (within 2°C) how much warming would result from a doubling of CO2 in the atmosphere (Crawford 1997).

As a part of the project "Can we know what to do about AI?", I've summarized my initial impressions of Arrhenius's predictions and the impact that they might have had. The object level material is all draw from Wikipedia, and I have not vetted it.

• Arrhenius's chemistry was sound: the equation for how the Earth's temperature varies as a function of concentration of carbon dioxide is the same equation used today.
• For the most part, Arrhenius didn't model how increased carbon concentrations would impact other factors that influence the Earth's temperature. I don't know if this is because he wasn't aware of these, because he thought that they were sufficiently small to ignore, or because he didn't try to.
• Knut Ångström criticized Arrhenius's claim on scientific grounds, giving a different model which predicted no climate change from increased carbon concentrations. My surface impression is that Arrhenius was a much more accomplished scientist than Knut Ångström was. To the extent that this is true, I think that Ångström's view should be heavily discounted, but I haven't investigated further.
• While Arrhenius recognized that the use of fossil fuels could increase atmospheric concentrations, he underestimated how fast carbon emissions would increase (by a huge margin) because he didn't recognize how widespread fossil fuel use would become.
• People later thought that Arrhenius's prediction that atmospheric carbon would increase was wrong, because they thought that oceans would serve as great carbon sinks. It would be interesting to look into whether they had good reasons for thinking this at the time.
• Arrhenius predicted that global warming would have positive humanitarian impacts on balance, global warming now appears to have negative humanitarian impacts on balance. 

Taking this all together, based on my surface impressions, I think that this case study gives evidence against attempting to predict the far future being useful:

• To the extent that Arrhenius was right, he was largely ignored. 

• Arrhenius could have been wrong (the countervailing theories could have been right), but this warrants further investigation. 

• If, in the subsequent years, people had started burning fossil fuels more with a view toward giving rise to positive humanitarian impacts, they would have exacerbated the potential negative impacts of climate change.