> 4. At different points in the Earth's history it has been both substantially hotter and colder than it is now;
The atoms in your house were much hotter when they were being formed by fusion inside a star, but that doesn't mean you'd be happy about someone committing arson.
I'm saying it's not really relevant whether Earth has experienced higher temperatures before, what matters is how long it will be able to support 8 billion humans for.