In order for pure damage spells to stay competitive with standard opponents' HP, you need to pour on the bonuses. Draconic bloodline with its +1 per damage die goes quite a bit of the way.
But already at 5th level, where you'll be doing 5d4+5 (Burning Hands; average 17.5, assuming failed save) or 4d6+4 (Scorching Ray; average 18) with your fire spells assuming Draconic bloodline, you're falling behind. Monsters of CR 5 have around 55-65 HP typically, so you'd need lots of spells to solo one. Your typical Half-Orc Barbarian can deal an average 20 HP on a successful Power Attack with a Greatsword. You're spending spell slots, and you're still not contributing as meaningfully as your mundane counterpart. That's feeling useless as a caster, right there.
For that reason, I'd do several things:
1. Interpret "fire-themed" loosely. A lot is in the fluff, in the way you describe the things you do. Don't fixate on pure fire damage, but mix in some other options as well, especially debuffs and battlefield control. Glitterdust (good spell) can easily be imagined as "a shower of embers and sparks clinging to and singing clothing, armor, weapons and hair". Stinking Cloud can be described "I pick a handful of smouldering coals out of nowhere and hurl them. A choking black smoke rises and covers everything". Even Web can be visualised as "clinging tendrils of whitish smoke shot through with fire. Enemies within the firey smoke cannot move easily for risk of burning themselves." Invisibility: "I seem to spontaneously combust, leaving grains of ashes so fine they almost cannot be seen floating on the wind where I go, nigh-invisibly outlining my form". Even Charm Person: "I ignite an inner spark within him. A steady warmth manifests in his heart whenever he looks at me. He cannot but be moved by the comfortable feeling." [replace with "firey passion" as needed] Etc.
2. Tack on some 'rider effects' with your damage spells. PF provides quite a few nice metamagic feats that add a debuff to the damage. Dazing Spell is my favorite, but Toppling Spell (ask your DM to apply it to non-force spells; shouldn't be a problem balance-wise) and Sickening Spell are likewise good. Lingering Spell plus Extend Spell adds some nice battlefield control to instantaneous damage spells like Fireball.
3. Also, get your damage up, so the damage portion of your casting actually accomplishes something. Ask to be allowed certain 3.5 feats that increase your caster level: Bloodline of Fire obviously, Fiery Burst, maybe Spellcasting Thematics. Metamagic: in PF, Empower is a trap of a metamagic feat. Maximize is worse, the spell level cost is just too high. You'll fare very well with Intensified Burning Hands though.
4. Remembering (1), keep other options handy, in case you run into fire-resistant enemies. Also, keep your knowledge skills high, so you know whether your enemy is resistant before you waste a Scorching Ray.
