We haven't lost all our hair (just ask John Kerry) but we have less because our ancestors evolved on the savannah, where heat regulation is a prime concern. Having too much body hair is also a hindrance more than it is a blessing -- you can take off a winter coat when it's hot, but you can't as easily shave. That makes it easier for us to inhabit a wider variety of climates.
Savannah is really only hot in the summer.
Then why haven't the rest of the animals lost their fur?
That is an interesting comment. Hair on the body disappeared but why did hair on the head remain thick. People who evolved in cold climates have also lost most of their body hair. Surely that hair would be added protection. Many, if not most, of the animals on "the savannah" have hair all over their bodies. Surely they have a need to regulate heat but haven't evolved.