Body size

From my understanding the PETM resulted in dwarfism in mammals (http://westerndigs.org/global-warming-caused-dwarfism-in-ancient-american-mammals-fossils-show/), 30% in fact, not the annihilation of all mammals. We have the biotechnology, or will have soon, to select (or mutate) for dwarfism. If that is possible, then humans could adapt. Here are 2 examples where humans have evolved to suit different environments;

http://en.wikipedia.org/wiki/Homo_floresiensis (just for arguments sake I am going to take the average height of females at 167cm, LB1 was 110cm. That is 65%, damn close to the 30% reduction mentioned earlier)
http://en.wikipedia.org/wiki/Yaghan_people These, on the other hand, evolved to handle colder temperatures through a metabolism change.

Secondly the way I see it, a re-occurrence of the PETM would result in areas that are inhospitable to humans, but not all. At 3C (the beginning not the end), you have large areas that would be inhospitable, in summer. Anybody not prepared would have little chance of surviving. So they will migrate.
Initially those areas (Southern Chile, Antartica, Greenland etc) that are survivable in a heat events would be very violent and dangerous places. Given the over population, lack of skills, infrastructure, poor soil and resources it would be hell on Earth.
A society that had prepared, was structured, and was willing to wait would be rewarded without firing a shot. At 4-6C then it is time to move, depending on the community’s location.

But survival in these sorts of hostile environments is going to be related to body mass. With adequate planning we can adapt.

We don't need a medical breakthrough to regulate our height (well we do, if we wanted to mutate). I want to make it clear that some of these solutions for size are unpleasant and ethically dangerous, that is why a safe mutation would be preferable. Realistically though I doubt it could ever be done without some unintended negative side-effect. 
When the choice is for the extinction of man or, at best, the reduction of man back to the stone age and all the violence that that implies, some radical discussions are warranted. That is why I am offering the following as different means to restricting body mass;

Calorie restriction. Calorie restriction reduces body mass and lowers metabolism. Therefore it reduces body temperature. It's a tough pill to swallow.

There is already a treatable condition called Acromegaly (search the Mayo clinic). Acromegaly is a hormonal disorder that develops when your pituitary gland produces too much growth hormone during adulthood. There are a variety of treatments for it. Could those treatments be used to artificially reduce growth?
Realistically though, that would need applied early in life to kids that are above the average height for their age. Though who knows what the side-effects might be. Obviously this is hugely contentious topic, it would take a very hostile environment before I would give my kids any sort of drug.

Next is natural selection. Natural selection takes eons. That would be a burden on any community. 

Unnatural selection. There is no way I would ever condone an aggressive selection process. It would make us no better than the Nazis. Also I don't believe in the servitude of women. So why bring it up? In a community where everybody was a parent to every child, and that it was accepted moral and cultural practice, encouraged "partnerships" have been used for centuries. If you look at the variety of forms within domesticated pets you can see the power of encouraged partnerships. Sounds foreign and it is. But survival would depend on having children that could survive.

Lastly, perhaps it should be firstly, I see adoption. All things considered, this is ethically the most attractive. Adoption on the basis of body structure, and other traits. Which stated, or implicitly is how it works now anyway. There will be a human tide of suffering, rather than add to it, wouldn't it be better to help some of them?

So initially the cooling of a body mass for the current generation would need to be dealt with using current technologies. Those technologies will eventually breakdown, the next generation will have to look at things differently. That will be an ethical issue for them to resolve. To cool the body using current technology would require a number of other techniques covered in the "Body temperature" post on my site. I am hoping that people will post suggestions that I can add to within the content.

Correctly planned for we are not going extinct, we will adapt. But there is a truly positive spin on this. Should humanity survive, the lessons we will have learned from the history of our foolishness, would surely give us spiritual wings. Is a bird any less an animal for having evolved from a maniraptoran dinosaur? I say it is more, because it has a better perspective.

Again, I hope that none of this is taken offensively. It is meant as an ethical discussion on planned adaptation.