Okay! So, my strategy was to starve my population to 5 and stock up to 35 wheat before attempting to remove all the trees.
With that I was able to get down to 5 trees before cutting the rest down, which left me plenty of space to quickly replant enough trees to stabilize the climate.
Then I starved them down to 2 people to get rid of all the larger houses. After that, I rebuilt up to 8 people, and spread out the houses before stocking up to 80 wheat.
At that point, I cut down all but 2 trees and spent a few turns waiting for the temperature to slowly rise.
At about 75% of maximum, only one fire spawns. At which point I instantly planted all the trees I could without any being next to the fire. You wanna come back below the current temperature so the lightning will stop.
By this point, the "uh oh, I think we broke the environment" quest should be up. The fire will spread. Once it destroys something, it will bring up the "survive the fires!" quest.
From there, just focus on cooling the climate by planting as many trees as possible and the fire shouldn't spread that much.
When the last fire goes out, you will get here!
Uranus got a new moon :D