Here’s the Wikipedia article on fission. It’s a rather different process:
I don't think anyone knows for sure what is going on down there.
My theory is that it's both critical and quiescent, with a violent dynamic at play. Gravity will concentrate the heaviest and least stable elements as you'd expect. As that happens pockets of dense matter in close neutron proximity will approach critical and heat billions of tons of matter which then convects outwards, dispersing the mixture. Think of a lava lamp.
edit: ah, just read the title of the link posted in the top level comment. apparently it's "half of the heat" :)