Fire in the game could use an upgrade comparable to how water was eventually improved in the Aquatic Update. Right now it just burns stuff away without leaving a trace... suffice to say it could use some work.
-Now, when fire burns a block, it generally produces a layer of ash on a surface directly below it. Ash can accumulate like snow layers, and slows movement. (Perhaps it can be collected for a crafting recipe of some sort. Maybe rain or water washes it away? Or maybe it can be used as some sort of fertilizer.)
-When fire burns wood blocks, it has a small chance of creating charred wood instead of turning the wood to ash. This is a new wood set, which includes stripped charred logs, charred logs, charred planks, and various variations thereof- however, the only way to obtain these is through burning them. They can only be collected with silk touch, and otherwise produce ash when broken. Charred wood is slightly more durable than normal wood, grey, and (of course), fireproof.
-In this manner, when a fire occurs, it leaves burnt logs and piles of ash, a sign that it's been there. (I've included some simple concept art- the wood is just the oak wood textures in grey scale. (Note how foliage can also produce ash when burned.)