Path of Burning Hatred

This type of barbarian channels his anger into fire around him, and uses it to empower his hits. It also burns him slightly, but in a rage the barbarian doesn't notice.

Burning rage

Starting when you choose this path at 3rd level, you can go into a rage, and when you do your enemies take 1d4 fire damage when they attack you. Your barbarian damage is also considered fire when it comes to dealing damage.

Flame consuming rage

Beginning at 6th level, while raging you are wreathed in flames. Anyone within 10 feet of you takes half of your barbarian level in fire damage, as well as you do. While raging you also gain resistance to fire damage. 

Eternal Anger of Flame

Beginning at 10th level your rage is so powerful it has trouble going out. Your rage won't end so long as you are near something that is flammable and has been burning because of your rage, or a creature has taken damage due to being within your rage. 

Burn through death

Starting at 14th level, your rage aura of fire is so powerful it is hard to stay within the confines of it for very long. Your aura extends out to 30 feet, and the fire damage is now equal to your barbarian level, however you take the same damage you would as if it were only half your barbarian level. Finally, as a reaction when a creature drops you to 0 HP, you can have the fire restore you. You explode in flames as everyone within 60 feet takes 8d8 fire damage and must make a STR saving throw (DC equal to 8+your proficiency and CON modifier). If they fail they take full damage and are knocked prone, if they succeed they take half damage and are not moved. You are then put at 1 HP and your rage ends. Anyone who dies from your restoration to 1 HP or your barbarian rage is disintegrated after 1d4 rounds plus their constitution modifier.