Path of the Raging Inferno

Some barbarians revel in the heat of battle, but barbarians that follow the Path of the raging Inferno are the heat of battle. Their pure, unadulterated rage emanates from them as extreme heat or even flame as they scorch the battlefield with their fury.

Angry Blaze

Starting at third level when you take this barbarian path, your anger can erupt from you in palpable, sudden bursts of flame. When you begin your rage, every creature within a ten foot radius centered on you must make a Constitution save with a DC equal to 8+ your Constitution Modifier+ your Proficiency Bonus or take 1d10+ your con mod in fire damage.

Rageforged

Becoming used to your own raging heat, at level 6 you are resistant to fire damage. Additionally, any save you make  against an effect dealing fire damage is made with advantage.

Flare Leap

Beginning at level 10, you can launch yourself up to 30 feet with a burst of flame as an action. Any creature adjacent to you when you jump or land must make a constitution save with DC equal to 8+your proficiency bonus+ your constitution modifier or take 2d10 fire damage, taking half as much on a success.

Inferno Avatar

At level 14, your ragefire is extreme, as is your control over it. Starting when you rage, you are affected by the Investiture of Flame spell. This lasts for a number of turns equal to your con mod or until you lose concentration. This is the only effect that bypasses the "rage ends concentration on a spell" clause. The save DC for this spell is equal to 8+ your proficiency bonus+ your con mod.