I think it would be wonderful to add global warming in the late game, to add a difficult challenge which breaks the boring predictable linearity of progress. You could have it as an option/mod so that you can choose to play without it if you find it annoying. Civ isn't just about conquering or going to space, you're supposed to build a Civilization "that will stand the test of time".
Of course a global warming expansion or mod needs to add more gameplay. You need some kind of world congress, diplomatic climate change agreements, social policies and probably an additional victory condition. Or you could simply have it so that a Time victory requires all remaining Civs to cooperate if they wish to survive. Maybe there could be prestige victory (competition) about who can reduce their emissions most and sequester carbon most. I'd say that any game wishing to simulate the future (based on our current situation) needs to deal with several challenges.
Challenges (problems to solve):
- The ongoing massextinction of flora and fauna. The worst case scenario would be the disappearance of for example bees and important pollinators, making agriculture incredibly work intensive and increasing the risk of droughts and famines. This could be represented by a global reduction in food yields, that has to be overcome by inventing GMOs and other various technical solutions, and of course reducing emissions. Also, overfishing is currently a big problem in a lot of ocean and coastal areas. Some scientists argue we need to stop using large scale fishing fleets and go back to smaller scale fishing.
- Increased desertification and soil degradation due to intensive agriculture and reduced precipitation in a lot of areas. This could be represented by overall reduced food yields, plains turning into deserts, grasslands turning into plains, forest regrowth reduced in these bordering areas. The players would have to reduce their emissions to limit the rate of change, and adapt by big technical infrastructure programs, improved hydrological management. Reduce/alter production of goods that require lots of water, like Cotton and prioritize stable Food production.
- The melting of land-bound glaciers will reduce the more or less stable water supply for some of the world's largest rivers, leading to more and more drastic water shortages, in turn leading to droughts and starvation. This could be represented (in-game) by all tiles adjacent to rivers getting minus to food. Today's "current" of refugees is nothing compared to what you'll be seeing in 10-50 years. In the game this could be "random" movements of population from cities that have drastically reduced food yields to cities close-by, leading to overpopulation in those cities (not enough happiness/amenities/housing etc), leading to unrest.
- Many dry places will get drier, some tiny and (agriculturally) insignificant cold wet places will get slightly warmer but also a bit more wet (like Northern Scandinavia). In the game you'd have some Tundra turning into plains, and snow into tundra, sea ice features will start to disappear. (Of course IRL we're talking about the winter's oceanic ice sheets lasting for shorter durations.). Some northern or southern plains could turn into grasslands, of course not those closest to the equator/Mediterranean.
A suggestion for game mechanics:
How do you represent emissions and the rate of climate change? I guess you could have an "invisible" value, which accumulates points for all Civs actions.
So every coal and oil resource with an improvement will add to this sum, every turn. The oil and coal consumption (and thereby emissions) can be calculated by multiplying the population of every city with the number of coal/oil that is improved within its border, +1 for every citizen assigned to work such an improvement. Every turn you'd accumulate more "points" and the rate of climate change would depend on how high the current sum has gotten. If a city doesn't have any oil/coal itself but has any or both traded from another city or Civ, it would also contribute.
Depending on tech, additional buildings and improvements would multiply the number of emission points.
Example:
A city of 10 population could add emissions by:
Each oil or coal resource improved= 1*10
Each oil or coal resource worked = 1*10
Each industrial district with a factory or power plant = 1*10
With motorized agriculture, every farm = 0.5*10
Every motorized mine = 0.5*10
Every tourism point could add as well.
Other buildings/districts also...
Edit: Read up on nuclear weapons and they don't contribute to warming, my bad.
Apart form coal/oil/fossil fuels you can also take land use into account. Every forest/jungle tile that has been chopped/replaced by district would add points to the Emissions sum.
The effects of global warming would lag behind, meaning that even though you increase the rate of emissions, you wouldn't see the effects right away. You'd have to establish certain threshold levels that bring effects. Once a higher threshold is reached, the rate of climate change (bad stuff) increases.
So how would you win this Prestige victory? Or at least reduce emissions (the increasing sum of emission points)?
Replace old improvements, remove those which bring a lot of emissions, tech, stop working certain tiles, modernize or reduce your army/fleet, plant forests/restore wetlands, new buildings/improvements to sequester carbon, new social policies which reduces Wealth/Gold/Food/Production output in exchange for reduced emissions. And so on...
Every action that reduces your emissions (the addition for each turn) and the total sum accumulated (sequestering carbon) would give you Prestige points.
For more info on climate change, I really recommend checking out SRC (Stockholm Resilience Center) and their director Johan Rockström. He's a climate scientists, not a politician, and talks a lot about Planetary boundaries (the environmental and ecological limitations we had to cope with).
http://www.stockholmresilience.org/research/planetary-boundaries.html