Here's a Pyromaniac Combat Sorcerer:
Intelligence 5, Occult 5.
Performance 5, at least Charisma 3. Take the "Burnt Offerings" shaping ritual from "Pact with an Ifrit Lord".
Take Resources 3 or 4, as well as the "Suzerain of the Endless Flame" and "The Burning Name" merits.
Learn Flight of the Brilliant Raptor, though there is no need to learn it as a control spell.
Whenever needed, you make a Resources 2 burnt offering, rolling 8 dice against difficulty 3. Without an excellency that's only succesful on average, with a full Excellency you can easily gain 4 net successes and thus expect 5 sorcerous motes from that.
In combat, you use "The Burning Name" to attack by summoning flames from your eyes, limbs or mouth. That's a short range mundane thrown weapon, using (Intelligence + Occult) for attacking.
If you want to finish off a dangerous enemy, you use Flight of the Brilliant Raptor. You need 12 motes (thanks to Suzerain of the Endless Flame) and probably start out with 5. Using a full occult excellency for your shaping rolls, that's very likely doable in a single round.
The attack roll is (Perception + Occult), so you want decent Perception and will probably use an Excellency on it. Effectively this is a long-range attack that adds your Willpower to your Raw Decisive damage.
It also leaves behind a bonfire, so the enemy likely has to make a difficulty 5 (stamina + resistance) roll at least once or take 4L damage.
Investment at character creation:
6 skill points, 4 bonus points, 6 attribute points (in 2 different categories), 7 merit points, 1+ charms (Terrestrial Circle Sorcery + other spells).
If you instead want more control over fire (and less collateral damage), you can take the shaping ritual where you draw motes from flames. This will most likely increase your casting time for Flight of the Brilliant Raptor to two rounds until you have higher Essence, but it also allows you to neatly extinguish most fires toe fuel your spells.
Other useful charms for this are Ancient Tongue Understanding (just as a prerequisite, later you can use it for free bonus successes on occult/shape sorcery rolls) and Supernal Control Method for one free Occult Excellency per scene.
Masterful Performance Exercise is a nice basic charm, its one automatic success effectively equals one more sorcerous mote per combat.
Ask your GM whether your flame attack (which curiously enough doesn't have the Flame-tag) can be enhanced by thrown charms. RAW supplemental charms don't apply if you don't use their ability, so sadly that's not the case without GM-permission.
