Path of the Burning Soul:
Fist of the wildfire
When you pick this subclass at 3rd level, you give up on the use of weapons and armor to dedicate yourself completely to perfecting your body and senses. You lose all weapon and armor proficiencies granted by the Barbarian class, in exchange, you gain proficiency in both Athletics and Acrobatics skills. If you alredy have proficency in one of these skills when you choose this subclass, pick another skill of your choice to be proficient in instead.
Additionally, your unarmed strikes now deal 1d6+your Strength modifier. The die changes as you gain levels in this class, at level 6 it becomes 1d8, at level 10 a d10 and at level 14 a d12, whenever you deal damage with your unarmed strikes, you can decide to deal either bludgeoning or fire damage.
Overheat
Also starting when you choose this path at 3rd level, while raging you can make an unarmed strike as a bonus action on each of your turns, furthermore, your unarmed strikes deal 1d4 extra Fire damage while raging. Although, whenever your rage ends, you suffer one level of exhaustion and you take fire damage equal to your character level (this damage ignores all immunities and resistances and cannot be reduced in any way).
The effects of the levels of exhaustion gained through this feature are ignored while you’re raging (altough you still retain the exhaustion levels).
Superior martial arts
Once you reach 6th your unarmed strikes count as magical for the purpose of overcoming magical resistances and immunities, furthermore you gain resistance to fire and cold damage.
Cauterize
Starting at 10th level, as a bonus action you can expend either five of your hit dice or one use of your rage fature to either regain a number of hit points equal to one roll of your unarmed strike die+your constitution modifier or end one level of exhaustion on yourself.
If you play with fire…
Starting at 14th level, when you take damage from a creature that is within your reach, you can use your reaction to make one unarmed strike against that creature. In addition, you gain immunity to fire and cold damage.