If all humans and animals on earth were suddenly gone:

Global Warming still would increase exponentially for at least 300 to 500 years before it slowly petered out from no fires and no methane from humans and animals. This is a scientific fact.

So, even with no human interference in the environment at all we would be facing a very difficult 300 to 500 years even with no animal or human methane from feces. Methane is even more dangerous in it's effects on the upper atmosphere than CO2 is. And as the Arctic and antarctic melts everything that died (plant, animal and human) that turned into methane underground and underwater will be released (as it is now) into the upper atmosphere of earth.