First off, Andre (down in another forum) seems to be adamantly against the whole idea of global warming. So the basic assumption of your question isn't accepted by everyone (I happen to agree with your assumption but I'm not a paleoclimatologist) which is not uncommon in science.
Secondly, we have historically and consistently underestimated biodiversity, especially at the "low end" - the microbiology end - since Joseph Lister was around. Because we don't have a great handle on it now, any projections about this sort of thing would be total speculation. Garbage in garbage out.
My personal point of view is: from an ecological successionary point of view, the guys who gets there first usually wins. This means if the environment changes the spores (or sclerotia or whatever) already in place have first shot at exploiting the new environment. Since we don't know what we have now in place, it makes it hard to predict. YMMV.