Treat the wand like it came from a blacksmith's forge
While some blacksmiths don't use gloves at the forge, others do. And they generally wear them for very short exposures to heat (a wand going whamo should count).
Leather gloves won't be enough to protect against very high heat (fireball spells) but it will protect you from radiant heat near the wand. You also want a leather apron, some kind of safety glasses, and boots.
About the Leather gloves - Experienced blacksmiths will sometimes recommend no gloves. I strongly recommend a glove on your not-hammer hand. At least just to start. This will prevent burns. Later, as you get more experienced with blacksmithing you can decide what you like.
About the boots - This is important because you are going to be dropping hot pieces of steel and you want a solid pair of boots to protect your feet from burns. If you plan on handling heavy pieces of iron and steel then I would go with steel-toed shoes.
So lots of safety gear to start then you can reduce it when you get used to spellcasting.
This site also recommends wolf jaw tongs (not plain jaw/flat). I'd recommend some made special to firmly hold your wand near the base. If blacksmiths can use these to hold on to heavy metal glowing like a miniature sun, and then be able to manipulate the metal on the anvil, you can use them to hold your freaking wand still while you cast.
Remember, the apron and boots and eye coverings (if possible) are for when you are an idiot and drop the hot wand as soon as something blasts out of it.
Okay, so this covers you for basic fireballs. Now, what about the Sheeeaaaaah-Moogatee-Hah! spell?
Okay, this requires some setup. I recommend the following:
- A large barrel made of thick oak plated with metal with a 3-4 inch hole drilled near the top.
- Fill with water such that it will later reach up to the bottom of the hole.
- Get in the barrel with something protective on your head.
- Put on a leather glove.
- Stick your blacksmithing tongs out the hole and grab the wand.
- Make sure that under the wand is a bucket of water or a pile of sand.
- Cast the spell.
- Drop the wand.
Alternatively...fire that sucker from a stone castle window or rampart, the kind archers shoot out of. Have a trusted running retrieve the wand after it drops in the water/sand and is cool enough to pick up with tongs or a gloved hand.
No, it's not melee-worthy like your fireball and other low to high level spells are. But if you want the nuclear option, you need to build a launch point. This completely violates your requirements, but seriously, do soldiers with fire launchers run around with them in combat? No, they use a sturdy base, sometimes one that is somewhat portable. If you fight with a canoncannon can you carry it in your pocket then pull it out and boom? Nope.
Remember, your question was protection for a fireball spell. And you state: "casting the fireball spell generates enough heat to cause 3rd degree burns on the unprotected hand and wrist." My solution easily protects against that.
