About 130 degrees Fahrenheit (55˚ Celsius), with proper hydration. However this depends on many things, such as the length of exposure to the heat source or how used to the hot temperatures is the individual person.
For example, a person who lives nearby a hot desert, or is used to desert temperatures will obviously resist heat longer, than a person who is relatively used to cold temperatures.
Some Detail Edit
The above explanation applies to outside body temperature. If we were to talk about internal body temperature, in 1987, I survived a heatstroke, during which my body reached an internal temperature of 108˚Farenheit, which is the extreme upper limit of survivability. It has been medically documented that the body's internal organs start to break down and die at temperatures of 108 or higher.
For example in this page: http://www.blurtit.com/q616156.html
A user commented: "Well I'm not sure what the highest temp that the human body can "survive" in but i know at this point in time i am currently working in a sustained heat of 67 to 73 degrees celsius in areas it reaches 78 to 84 degrees Celsius the thermometers even shut down ive even seen a respirator face plate fall out it was a 3m PAPR with no previous issues just caused from the heat oh yea we were tyvek suits and PAPR's non of which is heat reflective or resistant"
If we convert 67˚ Celsius to Farenheit it would add up to 153˚ Farenheit. So to be fair this individual is exposed to an environment that its unlivable to most people. But with proper clothing he can survive. This doesn't even count the people who expose their lives exploring and studying volcanoes.