This is a hostile place for humans - both temperature and a lack of pressure pose the biggest threat.
The earth's atmosphere is divided into 5 layers. We live in the troposhere. Felix jumped from the stratosphere.
Air pressure is nearly nonexistent at Felix's jump altitude of 128,100 feet - this means 99% of the earth's atmosphere was out of reach. Normally the atmosphere cools a few degrees with a rise in altitude. Flying a jet at about 35,000 ft is typically where temperatures drop off dramatically to -50F or even -70F degrees.
The cooling trend slows down as you enter the initial layer of the stratosphere, which is never at an exact altitude. The stratosphere just like any layer of the atmosphere starts and stops at various heights depending on where you are on the planet. These layers are temperature dependent. So Bobby McGee at the equator will give a report on the altitude of the stratosphere which will differ from Jenny McGoo's report because she lives at the North Pole. These variations change with the seasons too.
So the reason the temperature actually increases as you climb through the stratosphere is due to the ozone layer. Ozone molecules absorb energy and give heat back to the stratosphere. Still, it's very cold: 0 to -10F degrees.