Breaking fire down to intensity (material being burned) and amount of fuel (how much is being burned, per material weight) could work. Log would be non-intensive but have huge supply of fuel due weight. Just reduce the weight of log periodically until is gone - so “fire” entity would feed on the weight of the stuff it burns down, the material dictates how intensive fire is aka. how much weight is consumed per cycle on fire.
How fast and intense something burns depends on the item burning. Gasoline makes for a short intense burn. Logs would be longer, but generally require something else to start them (aka tinder). I feel this is mainly a refinement of the current system. Also think we should be able to construct chimneys out of rocks and something else (clay, mortar, cement). Most likely found in a hardware store, though clay is findable near a river… which are death on a stick with the current flyers near them.