School of Cryofire

Wizard who specializes in combining ice and fire magic.

Level 3: Cryofire Savant

 Level 3 Cryofire ability

Choose two Wizard spells that inflict cold or fire damage, each of which must be no higher than level 2, and add them to your spellbook for free.

Also, whenever you gain access to a new level of spell slots in this class, you can add one Wizard spell that inflicts cold or fire damage to your spellbook for free. The chosen spell must be of a level for which you have spell slots.

Additionally, the gold and time you must spend to copy a spell that inflicts cold or fire damage into your spellbook is halved.

Level 3: Frostflame

 Level 3 Frostflame ability

You have studied both ice and fire magic extensively and have found a way to combine the elements into one. This should not be possible due to their opposing natures, but you have bypassed such limitations through sheer focus. This new element is called Cryofire or "Frostflame" and it has the properties of both ice and fire.. 

You can use your action summon up Frostflame in your hand to light your way. Cryofire looks like a fire with swirling colors of both blue and orange. It gives off a soft light that ripples between it's two colors, it produces 15ft of bright light and 15ft of dim light. This simple form of Cryofire does not burn or freeze anything to the point of damage, but it feels unpleasant to the touch to anyone but its wielder. 
You may also use this Cryofire for offensive purposes. As an action, you can throw this Frostflame at a target within 60ft using your spell attack. On a hit, the target takes 1d10 Cryofire (look at Dual Nature for explanation) damage, and its Speed is reduced by 10 feet until the start of your next turn as it is slowed by frost. A flammable object hit by this spell starts burning if it isn’t being worn or carried. 
The damage increases by 1d10 when you reach levels 5 (2d10), 9 (3d10), 13 (4d10), and 17 (5d10)

Additionally, you can use your action to create solid Frostflame in your hands or in front of you. Solid Cryofire is clear and hard to the touch like ice, but it feels warm in cold temperatures, cool in hot temperatures, and looks like it has blue and orange fire dancing inside of it. It reads as a magical and it does not melt unless introduced to a concentrated source of heat (similar to a blowtorch) or it is submerged in water. You may create a number of cubic feet of solid Frostflame equal to half your class level rounded down. You can also sculpt the Frostflame into shapes and figures as you are producing it, how detailed they are depends on how well you can imagine and focus on what you're designing. Once you reach your cubic feet limit, you cannot create any more until you finish a long rest.

Level 6: Dual Nature

 Level 6 Cryofire ability

Reflecting it's dual nature, Cryofire has the capability to both harm and heal. You can turn spells that do cold or fire damage into Cryofire. A spell that uses Frostflame does no damage to allies, and if it hits its caster it heals them for half the damage dice (rounded down) instead of harming you. Any spells that do continuous damage, like Flaming Sphere, will not harm you or allies but will only heal the first round it's cast. If a spell does a different type of damage along with cold or fire, like Flame Strike, only the cold and fire damage are changed to Cryofire (so Flame Strike would do 5d6 Cryofire and 5d6 Radiant).
Enemies hit by a spell that used to do fire damage have their movement speed reduced to 10ft for the next minute, as a layer of frost crawls over them. They may make a Strength saving throw, with a DC of 10 + the spell's level, at the start of each of their turns to break out of the frost.
Allies hit by a spell that  used to do cold damage gain temporary hit points equal equal to twice the spell's level as the warmth of the Frostflame strengthens them.

Cryofire does both cold and fire damage, so it cuts through if a creature has resistance to one of those damage types and does double damage if they have one of those vulnerabilities. For example, if you did 20 damage with Cryofire against a creature with no resistances it does 20 damage, if they have fire resistance it does 20 cold damage, if they have vulnerability to cold it does 40 cold damage, if they have both fire resistance and cold vulnerability it still does 40 cold damage. 

You can change spells leveled 1-5 a number of times equal to your proficiency bonus. You may change a spell leveled 6 and up once starting at 11th level, twice at 15th level and three times at 20th level. You regain all uses of this ability after a long rest. 

Level 10: Frostflame Wreath

 Level 10 Frosflame ability

You can wreathe yourself in Frostflame for 1 minute as a bonus action. While wreathed in Frostflame you are protected from harm and do damage to enemies.

The Cryofire creates a barrier with a max number of hitpoints equal to your class level plus your Intelligence modifier, you can allow the barrier to absorb as much or as little damage as you wish. When the barrier reaches 0 hit points, your wreath disappears. You can replenish the barrier to by casting a spell as a Cryofire spell, the barrier will be replenished by a number of hit points equal to 5 times the level of the spell. 

The Frostflame wreath also does damage to enemies that come into contact with you. If you are hit by a melee attack, the attacker takes Cryofire (cold and fire) damage equal to half your class level (rounded up) + your Proficiency bonus.

You may use this ability a once per long rest. 
Starting at 15th level, you may use this ability twice per long rest.
Starting at 20th level, you may use this ability three times per long rest.

Enchanced Cryofire

 Level 14 Cryofire ability

The strength of your Frostflame has improved, and you can use your bonus action to enhance a Frosflame spell. You may only use each of these on one spell at a time. 
- Once per short rest, you may enhance the healing effects of a Cryofire spell to extend to your allies. If they are hit by the spell or choose to purposely fail their saving roll, they are healed for half the damage dice (rounded up). 
- Once per short rest, you may enhance the burn of a Cryofire spell. Enemies that take damage from the spell (for the first time) are set alight with Cryofire. At the start of each of their turns they take Cryofire damage equal to 1d12 + your Intelligence modifier. They will remain alight until they use their action to put the themselves out or another creature uses their action to put them out.
- Once per short rest, you may enhance the potency of a Cryofire spell. You may impose disadvantage on the saving throw of the spell, and creatures with abilities like evasion will still take half damage on a success. This spell cuts through resistances and creatures with immunity take half damage. 

Your Frosflame wreath is also improved. Enemies that try to target you while it is active will suffer from increasingly worse effects. 
Every consecutive round a creature hits you with a melee attack starts to form solid Cryofire on them.
-On the second round, their speed is halved.
-On the third round, they are restrained; they can break out of this by using their action to make a Strength saving throw against your spell save DC.
-On the fourth round, you force them to make a constitution saving throw against your spell save DC; if they fail, they are stunned.
-On the fifth round and on, you force them to make another constitution saving throw; if they fail they are petrified in solid Cryofire.
Every round that the creature does not attack you, their most severe effect is removed. For example, if they were stunned on round four, but did not hit you round five, they will just be restrained (unless they already broke out of it). If they don't hit you again on the following round, they will just have halved speed.
However, the effects will continue where they left off. If they did hit you again on the following round (round six), they would need to make another save or be stunned again.