Pyromancer is one of the two available skill trees for the Fire Staff Mastery in New World. Pyromancer abilities mainly focus on inflicting massive damage casting Fire spells and may leave the target Burning. Fire Staves benefit from Intelligence.
All Pyromancer Tree Abilities in New World
Pyromancer Tree Active Abilities

Incinerate
Cause a fiery explosion dealing 130% weapon damage and knocking back all enemies 3m. Catches enemies on fire dealing 3% weapon damage each second for 6s.
Costs 22 Mana. Cooldown: 12 seconds.
Upgrades:
Scorched: Each hit of Incinerate causes an additional stack of burning.
Cauterize Wounds: Restore 20% of Incinerate damage dealt as health
Flame Out!: Incinerate hits twice.

Flamethrower
Create a jet of flame from the tip of staff dealing 50% weapon damage each second. Each hit catches enemies on fire dealing 3% weapon damage each second for 6s. Cooldown: 8 seconds.
Upgrades:
Fire's Reach: Increase the range of FlameThrower by 50%.
Infernal Flames: Increase the base damage of FlameThrower by 25%.
Pyro Dancer: Flamethrower has no cooldown.

Burn Out
Dash through targets dealing 129% weapon damage on hit. Passing through a target will catch the target on fire applying a Burn that deals 10% weapon damage each second for 8s.Cooldown: 20 seconds. Costs 30 Mana.
Upgrades:
All In: Fire Staff cooldowns are reduced by 5% for each foe hit by Burn Out.
Heat It Up!: Burn out goes 50% further.
Pyromancer Tree Passive Abilities

Pyromania
While holding a Fire Staff and below 50% max health: damage is increased by 15%.

Heat Up
When you block a Melee attack, restore 5% of your max mana.

Kindle
Burning lasts 20% longer.

Trial By Fire
When you are struck, create a field of fire around you dealing 5% weapon damage to all to nearby enemies in a 4m radius. Activates when struck in battle and lasts for 10 seconds. (cooldown 120s.)

Let It Burn
Whenever burn deals damage, gain 30% Fortify for 2s. (Fortify reduces damage taken.)

Watch It Burn
Critical hits with fire staff abilities inflict burning, dealing 3% weapon damage each second for 6s.

Combat Speed
When you activate a Fire Staff ability gain 10% Haste for 5s. (Cooldown: 10 seconds)

Reheat
After 4s without activating an ability, your mana regen is increased by 400%.