So maybe combining the firepower and smoke cloud as a legendary action ?
---------------------------------------------------------------------------------
Firepower. The fire archomental starts every initiative with 5 Firepower. At the start of every turn it gains 3 Firepower. Whenever it is subjected to an effect or saving throw, it can choose to end the effect and automatically succeed the saving throw to burn the effect off. It can also end a magical effect within its attack range by spending 2 Firepower to incinerate it to nothing. When it reaches 10 Firepower, it must use the points in one of the following ways:
(1) Smoke Cloud. The fire archomental exhales a billowing cloud of hot smoke and embers that fills a 60-foot cube. Each creature in that area takes 11 (2d10) fire damage. The cloud lasts until the end of the fire archomental's next turn. Creatures completely within the cloud are blinded and can’t be seen.
(2) Fire Bolt. The fire archomental shoots a searing beam of fire for 33 (6d10) fire damage and 33 (6d10) force damage, up to a distance of 240 feet.
After this, its firepower goes down to 5. As the archomental’s Firepower increases, it visibly appears to produce more flames from its body, becoming a searing yellow to white-hot.
---------------------------------------------------------------------------------------
also made its melee attack:
Touch. Melee Weapon Attack: +6 to hit, reach 15 ft., one target. Hit: 26 (6d6 + 5) bludgeoning damage plus 35 (10d6) fire damage.
(seems odd using "touch" and "bludgeoning damage" together, maybe call it "fiery fist"?
I was thinking more something like this:
Firepower. A fire archomental's body contains Firepower, an energy it spends to power certain actions. The fire archomental starts every initiative with A Firepower. At the start of every turn it gains B Firepower; if this increases the archomental's Firepower to more than C it must spend enough Firepower that turn to reduce its Firepower to C or less.
Incendiary Resistance. Whenever it is subjected to an effect that allows a saving throw, the fire archomental can spend X firepower to burn the effect away, automatically succeed at its saving throw.
Actions
Firefist. Melee Weapon Attack: +## to hit, reach 15 ft., one target.
Hit: ## (#d# + #) bludgeoning damage plus ## (##d6) fire damage. The fire archoelemental can spend up to Y Firepower, adding ## (##d6) fire damage to the attack per point of Firepower.
Cleansing Flame. The fire archomental spends Z firepower to burn away a single condition or effect.
Fireball. ??
Incandescent Bolt. basically the Firebolt you proposed.
Bonus Actions?
Smoke Cloud. ??
Legendary Actions
Cleansing Fire. The fire archomental uses cleansing flame.
Purifying Fire. The fire archomental spends #Z firepower to burn away all effects and conditions it is subject to except for those it placed itself.
Smoking Fire. The fire archomental uses smoke cloud.
…and so on.
The amount of Firepower and how much Firepower various applications cost needs to be worked out, and may be tweaked to favour certain strategies (i.e. if the special attacks cost a lot more Firepower than the special defenses it'll fight more defensively).