Honestly, I don’t think anything we do will make a difference either way. The kind of investment that would be necessary is way more than people would agree to, even if there wasn’t an anti-environmentalist in charge of the US.
Since the planet may not be able to support human life indefinitely and life on other planets is not possible with current technology (at least for everyone on the planet), I think we should make a kind of internet that allows people to live on it full time, interacting with others as they would in the real world. To make things more efficient, people should be gathered together underground, almost like in a library, where the machines can look after their physical bodies and allow for a more immersive experience. Meanwhile the surface should be allowed to grow wild, without influence from humans at all. Machines would be able to control nuclear reactors and other sources of power to keep them safe and provide energy for the stored humans. You would be ‘online’ all the time, so you wouldn’t have to take care of your bodily needs at all – the machines would give you exactly as much nutrition as you needed and take care of waste. People could live their lives as they wanted, with children*, jobs, homes, everything you would do normally – you probably wouldn’t even notice that you’re not physically there.
While this may seem extreme, I also think we should find a way to provide permanent cloud cover across the earth during this time, in order to reflect solar energy and allow the earth to cool slowly over a hundred years or so.
*This is another reason why everyone has to be grouped in one big library – in order to preserve the human race, people need to continue having children. This could be done through artificial insemination, and the physical child would never live outside of the network. Everyone would look the same as they do in real life, in order to ensure a smooth transition with normal relationships once disaster is averted