Pyromancy

Other wizards are devoted to the occult and strangeness of specific schools of magic, the intricacies of Enchantment and Conjuration, or the versatility of Illusion and Abjuration.

You are not one of those wizards. You dedicate to study the myriad of ways in which you can set people and objects on fire, the fundamental flammable properties of everything and how to use magic to leverage them to your advantage.

Not all Evocation focused Wizards dedicate themselves to the destruction of their foes, but you most certantly do. 

Pyromancy 101

Beggining when you pick this school at 2nd level, you learn the basics of pyromancy. You gain the Produce Flame cantrip, and it counts as a wizard cantrip for you, but it doesn't count against your number of cantrips known.

Additionally, you can gain the ability to start fires with a touch. As an action, you can magically ignite a flammable object you touch with your hand—an object such as a torch, a piece of tinder, or the hem of drapes.

Flaming Motes

Also at 2nd level, whenever you cast a spell of 1st level or higher that deals fire damage or that summons a creature that deals fire damage, you can use a strand of the spell's magic to create motes of flames that surround and spin around you.

You create a number of motes equal to 1 + the spell's level, and as a bonus action on your turn, you can hurl one of the motes against a creature within 60 feet of you. Make a ranged spell attack, and on a hit, the creature takes 1d4 fire damage. When you reach 10th level in this class, the damage increases to 2d4.

The motes last for 1 minute, and you can only have motes of up to 1 spell at a time. You can use this feature twice, and gain all expended uses when you finish a short or long rest.

Amplify Fire

Starting at 6th level, whenever you cast a spell that deals fire damage, roll a d6, and you gain a bonus to one of the spell's damage rolls equal to the number rolled. 

Exploding Motes

Beginning at 10th level, whenever you damage a creature with one of your motes, you can dismiss an additional mote on your person (no action required). If you do, the damaged creature takes an additional 2d4 fire damage at the start of its next turn.

Mark of the Pyromancer Extraordinaire

Starting at 14th level, as a bonus action, you can mark a creature you can see within 60 feet of you with a sigil of expert pyromantic magic.

For 1 minute, one of your spells damage rolls and features that deal fire damage deal additional damage equal to your Intelligence Modifier. Additionally, if that creature is immune to fire damage, it instead becomes resistant to fire damage.

You can use this feature once, and gain the ability to do so again when you finish a short or long rest.