Recently people have been suggesting "climate crisis" which isn't going to help on the "less frightening" aspect, but I think that's a feature.
A global warming trend means more energy in the atmosphere, which in turn leads to higher weather variability, bigger storms etc. It doesn't mean everywhere on the planet will get a higher (pick your temperature statistic).
Sadly half kidding..
Showing more physical evidence and pushing developed plans is the only way forward I can see.
Except that the planet has been warming and cooling for millions of years.
To put into perspective:
Age of Earth: 4.6 billion years
How long Dinosaurs lived: 400 million years
Age of humans: 200,000 years.
The human species is literally less than a blip on the earth's historical radar. I'm convinced whatever we do to the planet, it will recover, like it always has. Humans not adapting? That's the real problem.
Understanding that the planet, if not the current biological configuration, is likely to be around much longer that we are doesn't seem to add much; at least to me.
This does not invalidate calling it "global warming". Just because it's happened before doesn't mean it's not happening now. When you hit the gas, do you restrict yourself from saying that the car's speed is increasing just because it's increased before?