Why didn't the polar bear change its color from white to black during evolution to absorb heat?
Polar bears do not have white fur - they don't have pigments in their fur hairs which makes them clear and translucent. The outer fur consists of hollow fibres, which shatter a part of the incoming light (the visible part) which makes them look white. This gives a very good camouflage in a white environment. 

It was initially thought (see reference 1) that the hollow fibers work in the same way as fiber optic cables and direct the UV part of the light (the visible was thought to be shattered) towards the black skin of the bears where it generates heat, but this hypothesis has been disproved. The UV part of the light is simply absorbed by the bears outer fur and doesn't reach the skin (see reference 2 for details).

The hollow hair helps with the insulation of the skin and can change the color due to environmental influences. The tend to get yellow after feeding on seals due to the fatty substances from the animals. There have also been reports from zoos that algae lived inside the hollow part of the fur making the animals more grey and sometimes even green (see reference 3).

Reference: 


Light collection and solar sensing through the polar bear pelt
Is polar bear hair fiber optic?
The greening of polar bears in zoos