As I remember, shivering triggers the release of irisin which both activates mitochondria and increases the population of mitochondria in at least some cells, notably fat cells turning 'white' adipose tissue into 'beige'. Mitochondria alone can be more efficient than shivering (which indeed uses mitochondria to produce the ATP needed for muscle contraction). Exercise also triggers irisin. There have been quite a few animal (mostly murine) studies, but nothing conclusive with humans.
On a mobile so no links, but google "irisin mitochondria".