Stoking up a fire involves physical interaction, not just adding fuel. She stoked up the campfire, poking the logs with a stick.
Pro Tip 2/3
Implies urgency
Stoke up often suggests an urgent need to enhance a fire, especially due to cold. We need to stoke up the fire quickly; the storm is getting worse.
Pro Tip 3/3
Not automatic
Stoke up means the fire needs manual help to burn well, as opposed to automatic fuel systems. Since the heater broke, we have to stoke up the old furnace manually now.