All penguins are well enough insulated so that heat is much more a problem for most of them than cold. 

For example, the emperor penguin is very heavily insulated with a thick layer of fat, and its feathers extend down onto its feet and onto its beak.  They usually have 77 feathers to the square inch.  Only the Adélie penguin is more heavily feathered.  Although much smaller, an Adélie penguin will begin to show symptoms of heat stress if the temperature rises above 32 degree Fahrenheit.  The possibility of a deadly heat stroke is then very high.

Imagine, the emperors are used to raise their chicks at  less than – 70 degree Fahrenheit.  No other warm-blooded animal is able to do that.  For them, it was so far the most secure way to do so.  Global warming is endangering this security on different levels.

The foremost huge ice shelf is cracking and is consistently decreasing. Even though the emperor parents have to walk less miles on their journeys between open water and breeding place, the ice shifting makes the journey way more complicated and dangerous.  If they fall into a crevasse, they will simply starve to death.  On the other hand, all predators have easier access to the breeding grounds.

This includes the rising numbers of tourists who come to the Antarctic, hoping to get their own shot of the appealing birds.

And of course, there is the over fishing of the oceans, oil spilling and so on.

The penguins have been fighting with the impact of climate change for years now.  We see the evidence of that battle in their inclining numbers.

Please check the Penguin Science and the Antarctica Project websites for deeper information.