One of the abilities, flame arrow, is not a 5e spell, so I updated the 3.5e version. I'm adding it to my ranger, sorcerer, and wizard spell lists. I'm on the fence about the "at higher levels" portion. That's an additional 10d6 worth of damage for each spell slot, which is a lot. Of course, I'm picturing using this to ignite 1 arrow each of a unit of archers in a mass battle as the initial shot in an attack, with each requiring a hit roll and not targeting the same thing. With the short duration, it's not reasonable for a single archer to go through all of them before duration expires.
Gauntlets of Heat
Very rare wondrous item, requires attunement
You must be a druid, bard or elementalist to become attuned to the gauntlets.
These gauntlets are capable of generating heat and fire upon mental command. You can use an action to expend some of the gauntlet’s 10 charges to cast one of the following spells without using any components, using your spell save DC.
Produce Flame (1 charge)
Burning hands (1 charge)
Heat metal (2 charges)
Flame arrow (3 charges)
For each additional charge you expend, you can cast the spells at a higher level slot.
The gauntlets regain 1d6 + 4 expended charges each day at dawn. However, if you expend the last charge, roll a d20. On a 1, the gauntlets blacken, crumbles into cinders, and is destroyed.
3rd level transmutation
Casting Time: 1 action
Range: 60 feet
Components: V, S, M (drop of oil and a small piece of flint)
Duration: 1 minute
You turn up to 50 pieces of ammunition (such as arrows, bolts, shuriken, and stones) into fiery projectiles. Each piece of ammunition deals an extra 1d6 points of fire damage to any target it hits. A flaming projectile can easily ignite a flammable object or structure, but it won’t ignite a creature it strikes.
At Higher Levels. When you cast this spell using a spell slot of 4th level or higher, you can effect an additional 10 arrows for every spell slot above 3rd.