I gauge how much fire something has based on how quickly its hp is falling. There's not much difference between 1 stack and 2, but a pretty big difference between 1 and 5, or 5 and 10. It's not perfect, but it's usually sufficient. EDIT: For reference, I believe 1 stack of fire drains 8hp/s, and each additional stack drains 2hp/s. So a 5 stack will drain a component's hp twice as fast as a 1 stack.
Also, it helps to be aware of what weapons are hitting you, and where. If you know how much a component has been hit with a particular weapon, it helps you guess how many stacks of fire are on it.