Over the last 1+ billion years the Earth has gone through many shocking events. Not just large changes in global temperature through ice-age and warming periods, but the atmosphere composition, asteroids, super volcanoes, and so on. If the ancient life form is still alive today after all of that, I doubt global warming would cause it to die.

Survivorship bias.

Lots and lots and lots of organisms died out during each of those changes. That things have survived so long is a matter of probability not inevitability.

My point was that a 2 degree change in the atmosphere now isn't so extreme for a 1+ billion year old organism as all the other history it has lived through.

I'm not trying to brush off the impact of global warming, I'm just placing it in the context of 1+ billion years of Earth history.

That's the point?

Anything that has survived for a billion years in a form that could still be considered roughly the same organism or a close descendant must have a relatively stable biochemistry and gene pool that is capable of surviving an extreme range of environmental changes - as close as you can get to a holy grail in natural selection.

Obviously its survival would not be inevitable; not even stars can survive their own age.

You have the math backwards. If there are events that kill 99% of everything and a million such events occur, then the survivors must be hardy in the face of shock. Global warming won't kill them; they've already been through incidents of far worse warming and cooling.

They maybe something in the soil of colder climates, desperately clinging on to existence, needing just a few degrees more heat to thrive. Either way, I find these articles about new life discoveries fascinating.

There are some bacterias in the russian permafrost that have been hanging on for a few hundred thousand years at this point (they aren't dividing, just repairing themselves in wait for a better environment, they're the same cells that got frozen up all that long time ago).

Possibly some simpler and more robust organism may lurk under arctic ice for a better time.