Wow that class is silly, it is a great example of how not to build a custom class.
What they got wrong:
The base class is wizard, the only loss from being pure wizard is familiar advancement(I am surprised that they didn't give you a fire elemental as a familiar...) and one feat every 5 levels(2). Now considering the sort of power they want from this(noticeable boost to spells with the fire descriptor((many many spells due to the feat))) it needs some sort of drawback, maybe -1 caster level to spells without [Fire], increasing to -2 at 5th and -3 at 10th...
Now the fort saves are good for a couple of feats right off the bat. It is a nice idea, what with the enduring heat and whatnot, but you really need to show restraint...
They added survival to skill and did nothing else, ummm, what? What does burning everything have to do with wilderness survival? And shouldn't the massive specialisation cost some level of academia? Skills are a great way to add some flavour, they could have dropped decipher and some knowledges, you could maybe justify escape artist and maybe intimidate and handle animal. Also, knowledge[planes] would perhaps make more sense as a prerequisite skill, looks as though they were just doubling up on arcana requirements...
While we are on requirements, this is basically a very powerful class, and you can take it at the absolute minimum level possible for prestige classes(obviously there will be exceptions, but there does seem to be a rule here) And it requires a single feat, which is massively useful to the class, and a skill, which you already needed for the feat, and spellcasting, which just goes to prove that the creator was playing a wizard, and not a sorcerer, which would have to wait till level 6 and therefore not been the absolute minimum level possible.
They seem to have fallen for the old trap of putting an ability in at every single level, some abilities just don't scale is such fine increments.
Blast wave? Flame Armour? Cute names, but they don't seem to have much in common with fire spells in D&D. Blast wave might work, but enough heat to knock someone over but not enough to do damage? These are just defensive abilities tacked onto an offensive class, if you are getting better attack spells then don't expect to get anything else... Flame armour is just wrong, +1 AC per level, and natural bonus too, where your only other source would likely cost you a constitution item? There are melee classes that would kill party members for that ability alone...
+1 caster level per 2 class levels, it is, really, a bit much. It only applies to [Fire] spells but still, considering that you still have full casting ability with the whole wizard list? No, just no.
Maybe if it was 1 per three and the class came with some penalty to casting...
Fire's Blessing? The wizard could blow all their feats on a +2 to DCs from a single school, you are getting level/3 to all elemental DCs? You will get +1 and you will like it! You will get down on hands and knees and praise the heavens for it! Honestly, kids these days...
I really don't get burning conjuration, well, I do, it makes your summoned tanks immune to fire, but from a flavour standpoint, where do they come from? Why do you care about summoning when you are worshipping fireballs? Meh, fire immune summons, what do I care...
Gift of the Blessed Fire... Wow, just wow... Fire subtype, okay, it has its drawbacks, lets you fireball yourself but that is not so very bad... Unarmed attack damage? unlikely to come up, and while the damage is a bit high, it isn't crazy... Damage return makes some sense, and it is within tolerable levels... No level limits? Do the mean that a fireball is not capped at 10d6? If so then they just ignored about half of the level limits on spell damage, this lets a level 15 deal more damage with a level 2 spell than a level 20 can with a level 9 spell, factor in metamagics and you just broke all semblance of balance...
That is a very odd breath weapon, but it doesn't seem to break anything, presumably there is a feat somewhere to exploit it that I don't know about...
Cheap metamagic combined with powerful low-level spells is just a really really bad idea.
Persisting Flame: Heh, cute, deal 150% damage but it takes a while to happen, not long enough for the victim to actually do anything about it, but still not instantly. Wanna know the really cute thing? While it looks like a disadvantage, but actually isn't, the delayed wording in this is actually a trick to bypass normal multiplication rules, now if they had just said +50% damage then combined with maximise it would have been 250%, but like this it is 300%, clever innit!
those 8 levels of having to rely on mere mortal spells to deal with fire immune opponents hurt, didn't they? but not to worry, now your only limitation is gone, half your damage is basically unresistable...
And the level 10 ability is probably not as bad as I would have expected, but wow is it broke. Your only weakness, cold vulnerability, that you picked up back at class level 5, along with your first unashamedly broken power, is replaced by 50% cold immunity, oh well, that'll learn your opponents to try to be clever. Oh, and what's this, you actually heal yourself when you fireball yourself? As if you had a cleric working full-time to heal you? I wonder if that 1d6+1 per caster level fire damage is half hellfire too? No matter, you are going to cast a metamagiced version anyway, so it doesn't really matter...
Compare, level 20 mage:
quickened maximised scorching ray: 72
maximised chain lightning: 120
2 level 9 spell slots lost 192 damage
Level 15 pyromancer:
quickened maximised fireball: 120 healing, 180 damage
1 level 8 slot, 300 damage, free action...
That class disturbs me in new and exciting ways...
Aaaargh, I spent too long critiquing a broken class and getting distracted by my other D&D session and missed the game!