This falls under the class of things that if they could happen, they already would have. The global temperature is not a uniform scalar modifier on what the temperature "would" have been without the changes. There are already hot spots and cold spots every year, continuously. There are already places in the ice that thawed out last year, and ten years ago, and during the Medieval warm period, and whenever it was warm before that. And we have not witnessed mass dieoffs due to disease from those events either.
It's like the concerns about high-energy collisions doing something terrible like forming micro-blackholes and eating the Earth. If that was a danger, it would be something Nature would already be doing and we'd be able to see it.
The ability to "infect" something is not a natural property that all bacteria have. It is something that has to evolve. A bacteria popping out of cold storage from half a million years ago precisely adapted to infect a modern animal would be every bit as weird as seeing a bacteria pop out of that same cold storage that was precisely evolved to live on Mars, or live on vast quantities of plastic, or otherwise adapted to conditions it couldn't possible have witnessed during its previous life.
It isn't absolutely, mathematically impossible. But it's not much worth worrying about. It's a science fiction storyline, not something that happens.
Now, if there were humans in such cold storage, I would be somewhat more careful. But so far in those cases where that has occurred we still haven't been wiped out. I haven't even heard of anyone pinning so much as a cold virus on pulling a cadaver out of a glacier. Links welcome if anybody does have such a story.
But it's a numbers game, right? A global thaw would be more likely to release a pocket of bacteria. It's like saying that just because a single bullet from a handgun didn't hit you, you ought to be safe when someone fires a machine gun at you.
And the Black Plague did happen to come by less than a century after the end of the warm period...
Per my point about evolution almost certainly prepping these bacteria to live somewhere other than the rather hostile insides of an animal, at the very least I'd modify that metaphor to someone shooting their bullets a few miles away from you, and pointed the other way.
I don't think we need to hypothesize that the Black Plague was some sort of bacterial refugee from the past; I've never heard anyone express any confusion about where it could possibly have come from, so it seems like a solution to a non-problem.
An asteroid can impact with the earth... Oh wait, that's happened already. Luckily, we haven't had such a collision large enough to kill us all, yet.
A plague could kill many people... Oh wait, that's happened already. Luckily, we haven't had a plague with enough virality and lethality to kill us all, yet.
It's like the concerns about high-energy collisions doing something terrible like forming micro-blackholes and eating the Earth. If that was a danger, it would be something Nature would already be doing and we'd be able to see it.
The ability to "infect" something is not a natural property that all bacteria have. It is something that has to evolve. A bacteria popping out of cold storage from half a million years ago precisely adapted to infect a modern animal would be every bit as weird as seeing a bacteria pop out of that same cold storage that was precisely evolved to live on Mars, or live on vast quantities of plastic, or otherwise adapted to conditions it couldn't possible have witnessed during its previous life.
It isn't absolutely, mathematically impossible. But it's not much worth worrying about. It's a science fiction storyline, not something that happens.
Now, if there were humans in such cold storage, I would be somewhat more careful. But so far in those cases where that has occurred we still haven't been wiped out. I haven't even heard of anyone pinning so much as a cold virus on pulling a cadaver out of a glacier. Links welcome if anybody does have such a story.