Harry stared into the fire, watching the logs burn and putting on more until he had a healthy hearth. *You know the state of firewood when there's no fire but the wood is seething with warmth anyway?
It makes a kind of sense, but I think perhaps not the one for which you are aiming. A hearth refers to both the metal grate within a fireplace where the logs are stacked (it aids in proper airflow) and also to large open fireplaces, the kind that would have once been the kitchen's cooking area. It does not refer to the state of the wood.
A hearth is a type of fireplace, typically open brick or stone. So while you can have a healthy hearth, it doesn't mean the hearth itself is burning, it would logically mean the hearth has a healthy fire burning in it. 'In the Scottish Orkneys, the little stone houses with their single large room and central hearth had an extraordinary range of built-in furniture.' -Stephan Gardiner.
Maybe you can say something like this: Harry's gaze was fixed on the fire, watching the logs crackle and putting on more until the yellow-blue flames rose into the smoke chamber.
I don't know how hearths can be healthy, any more than a chimney can be healthy or an andiron could be healthy. As others have pointed out, a hearth is simply a place for a fire to be built. I think you're referring to the fire itself. May I suggest that you substitute the word "blaze" for "fire"?
