I read in Tortora and Derrickson Anatomy and Physiology that :
Another type, called brown adipose tissue obtains its darker color from a very rich blood supply , along with numerous pigmented mitochondria that participate in aerobic cellular respiration.
From Wikipedia :
...brown adipocytes contain numerous smaller droplets and a much higher number of (iron-containing) mitochondria, which make it brown.
The conclusion seems to be that there should be some iron containing pigment in the mitochondria of BAT which (along with a rich blood supply) gives brown colour to the BAT.
What is the brown pigment present in the mitochondria of BAT ? Is it the uncoupler protein - thermogenin ?