> There's no long-term upper bound on how hot earth can get, and we're modeling uncharted territory: earth has never been as hot as it's going to get, while life has been on earth. So we really don't know how bad it will get.
Paleocene–Eocene Thermal Maximum [0]
The associated period of massive carbon release into the atmosphere has been estimated to have lasted from 20,000 to 50,000 years. The entire warm period lasted for about 200,000 years. Global temperatures increased by 5–8 °C. Paired δ13C, δ11B, and δ18O data suggest that ~12000 Gt of carbon (at least 44000 Gt CO
2e) were released over 50,000 years, averaging 0.24 Gt per year.
Since at least 1997, the Paleocene–Eocene Thermal Maximum has been investigated in geoscience as an analog to understand the effects of global warming and of massive carbon inputs to the ocean and atmosphere, including ocean acidification. Humans today emit about 10 Gt of carbon per year, and will have released a comparable amount in about 1,000 years at that rate.
Take a look also at "Abrupt climate change" article [1]:
Timescales of events described as 'abrupt' may vary dramatically. Changes recorded in the climate of Greenland at the end of the Younger Dryas, as measured by ice-cores, imply a sudden warming of +10 °C (+18 °F) within a timescale of a few years. Other abrupt changes are the +4 °C (+7.2 °F) on Greenland 11,270 years ago or the abrupt +6 °C (11 °F) warming 22,000 years ago on Antarctica.
[0] https://en.wikipedia.org/wiki/Paleocene%E2%80%93Eocene_Therm...
[1] https://en.wikipedia.org/wiki/Abrupt_climate_change