I've heard white fat is the stuff you DON'T want and brown fat is the one that is used for energy. What are some good ways of increasing brown fat?
You can somewhat successfully alter where your white fat is stored (subQ vs. visceral), but brown fat is like a separate tissue almost. It is more important in adults for small animals as it's thermogenic. While we have it, it's not huge. Apparently you can activate it by sitting in cold rooms with your feet in ice water baths. Shivering induces thermogenesis.
I think what you're asking is how to optimize fat burning via UCPs.
To optimize nighttime fat burning you need leptin sensitivity and good thyroid function, among other things.
A solid paleo diet should provide those things.
One of the best ways is cold exposure. It has been observed that rats exposed to cold temperatures eventually adapt by increasing the activity of their brown fat (1)(2).
This likely occurs in humans as well, one commonly cited example being Korean pearl divers who spend several hours a day in cold water have a large amount of brown fat (3).
Personally I love a freezing shower or a swim in some cold water, but I know it's not everyone's cup of tea.
(1)http://ajpcell.physiology.org/content/239/5/C208.short (2)http://jcb.rupress.org/content/23/1/89.abstract (3)http://www.jstor.org/pss/40511074