Infernal Bloodline

Descended from one of the 9 lords of Baator or another powerful devil, sometimes the blood of mortals runs hot.

When making an infernal sorcerer you might want to look at the suggested personality traits for tieflings and phoenix sorcerers. 

If you have a specific devil in mind, consider changing the fiery effects to another element (such as cold for Levistus).

Unholy Vigor

At 1st level, whenever you cast a spell of first level or higher you may gain temporary hitpoints equal to the spell level plus your charisma modifier.
Additionally you have resistance to fire and cold damage.

Burning Blood

Beginning at 1st level, as an action you can cause flames to course over your skin. Until the start of your next turn any creature that hits you with a melee attack from within 5ft of you takes fire damage equal to your charisma modifier.
As part of this action you can ignite one object that is not being held or worn

Born of Hellfire

The blood that fuels your spells burns hotter than most.
Starting at 6th level, when you roll fire damage for a spell you cast, you can reroll any roll of 1 on the fire damage dice, but you must use the new roll, even if it is another 1.
Additionally fire damage from your spells and abilities ignores resistances (but not immunities).

Aura of Ash and Flame

Your control over hellfire allows you to distort the air around you.
Starting at 14th, whenever you cast a spell of 1st level or higher you may choose ash or flame. The chosen effect lasts until the start of your next turn.

Ash: Thick black ash fills the air around you. A 10ft radius around you is considered lightly obscured (disadvantage on perception checks). Additionally ranged attacks against creatures in the area are made with disadvantage.

Flame: Fire courses along your skin. A 10ft radius around you shimmers with the heat radiating from your skin and is considered brightly lit. Any creature that starts its turn in the area, or when they enter the area for the first time on their turn, takes fire damage equal to half your sorcerer level plus your charisma modifier.

Overwhelming Presence

Beginning at 18th level, you can channel the presence of your ancestor, causing those around you to become awestruck or frightened. As an action, you can spend 5 sorcery points to draw on this power and exude an aura of awe or fear (your choice) to a distance of 60 feet. For 1 minute or until you lose your concentration (as if you were casting a concentration spell), each hostile creature that starts its turn in this aura must succeed on a Wisdom saving throw or be charmed (if you chose awe) or frightened (if you chose fear) until the aura ends. A creature that succeeds on this saving throw is immune to your aura for 24 hours