Actually, I think you have 'jumped the guns' so to speak on this subject, in saying that hair provides little to no insulation for an animal. This just isn't true.
In fact, in 2004, Harvard students shaved a camel, and found it's water loss due to sweat increased by over 30%. As well, it would seem logically correct, since physically most animals living in warmer climates have fur, such as Zebras, Giraffes, Lions, Tigers, Apes, Monkeys, Oxen, Antelope, horses, cows, hyenas, etc. You get the point.
There are many reasons that contradict apes `evolving` from quadrupeds to bipeds, losing their fur, etc. But I think for this particular subject, this information seems relevant.
Dennis.