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The solution to your magic wand problem is actually a staff... I love when one dumb trope is the right solution to another. Much like your chopsticks proposal, you are using a device to hold it away from you. The staff puts distance between your hand and the wand which is important when you dealing with limited insulating materials. While the heat of the wand is enough to cause 3rd degree burns, the head of the staff will heat up a lot at the end but much much less at the handle; so, slip the wand into the end of a staff and it's like holding a pot over a flame.

The solution to your magic wand problem is actually a staff and flowing robes... I love when one dumb trope is the right solution to another.

First the Staff:

Much like your chopsticks proposal, you are using a device to hold it away from you. The staff puts distance between your hand and the wand which is important when you dealing with limited insulating materials. While the heat of the wand is enough to cause 3rd degree burns, the head of the staff will heat up a lot at the end but much much less at the handle; so, slip the wand into the end of a staff and it's like holding a pot over a flame.

Your Wizardly Robes:

Ever notice how people who live in deserts seem to like to wear over-sized, full body clothing? The reason is because air is a great insulator. By wearing lose fitting wizardly robes your robe will heat up from the blast of heat, but poor contact between this surface and you skin means that it will not transfer that heat too you. Most robes will be made out of wool because it is the most fireproof natural fiber, but asbestos cloth is also an option in your 13th century setting for those wizards willing to trade good health for more powerful spell casting potential.

He could also use a cloak held out in front of his body to shield himself from especially powerful heat blasts. To keep his hand safe while doing this he could drape your cloak over the staff rather than holding the cloak directly.

To fully protect your body, a well to do wizard would also cover his face with a conical hat or hood (because it minimizes heat and maximizes coverage), a scarf, and some manner of goggles (yes, eyeglasses existed in the 13th century so goggles are a distinct possibility).

The Castle Problem:

An ideal staff would probably look a lot like the diagram below. The wand itself would be inserted into a glass or high-cone ceramic since these are the most heat resistant materials available in the middle ages. The holster would then be held by a steel head, preferably with seamingly decorative spines loops or other patterns to help it dissipate heat. Then the head would taper back, thick to thin. The steel closest to the head will get hottest so extra girth will help keep it from melting or warping when it reaches malleable temperatures, but the taper makes sure that less heat can spread back through the shaft. The handle itself would be wooden; since wood does not propagate heat well, this will further insulate you.

An ideal staff would probably look a lot like the diagram below. The wand itself would be inserted into a glass or high-cone ceramic since these are the most heat resistant materials available in the middle ages. The wand would be held inside of an oak holder. I know what you are thinking, "that is WOOD, you don't hold hot things with wood!" But there is good reason to use wood here. While materials like glass, ceramic, and steel all have higher melting points than wood, the wand gets very hot very fast. If you encase it in a hard and brittle material like glass or ceramic, the rapid nature of heating it up will cause a phenomenon called heat stress where the material will be encouraged to shatter as the inside becomes hotter than the outside. If this effect is extreme enough, which it sounds like it will be, then your ceramic holder will shatter killing your would be mage with shrapnel instead of heat. Making direct contact with steel, you are much less likely to have your staff explode, but the nature of rapid heating is again against you: A thin inner lining of metal will become molten and the metal around your wand will melt and blast the wand out the front of your staff.

So what makes wood so much better than steel? Specific heat, for starters. Oak has the highest specific heat out of any solid material available in the medieval period. Heating 1kg of steel to its melting point of ~1470°C requires ~670kJ at a specific heat of 462 J/kg.°C. Heating 1kg of oak to its ignition point of ~300°C at a specific heat of 2380 J/kg.°C also requires ~670kJ. This means that the ignition temperature of wood and the melting point of iron both require about the same amount of thermal energy; however, what wood does when it reaches its critical temperature is much more desirable. Wood only burns at 300°C in the presence of oxygen, but if your wand is fitted tightly in the oak then it can not burn until the OUTSIDE reaches 300°C. Instead the part touching the wand will continue to absorb heat until it reaches ~500°C at which point pyrolysis kicks in and the wood begins to anaerobically react by turning into charcoal, but even still wood does not violently explode when superheated, at worst the end of your staff will catch on fire, but the charcoal will expand and remain a solid medium continuing to grasp your wand well past the point that metal, ice, or ceramics would have found some way to melt/explode.

The Oak holster will absorb heat well, but not be good at dissipating it, and it will become brittle once it turns to charcoal. For this, you want to encase your Oak with a steel head, preferably with seamingly decorative spines loops or other patterns to work like heatsinks. Then the head would taper back, thick to thin. The steel closest to the head will get hottest so extra girth will help keep it from melting or warping when it reaches malleable temperatures, but the taper makes sure that less heat can spread back through the shaft. The handle itself should also be wooden; since wood does not propagate heat well, this will further insulate you.

The solution to your magic wand problem is actually a staff... I love when a dumb trope is the right solution to another. Much like your chopsticks proposal, you are using a device to hold it away from you. The staff puts distance between your hand and the wand which is important when you dealing with limited insulating materials. While the heat of the wand is enough to cause 3rd degree burns, the head of the staff will heat up a lot at the end but much much less at the handle; so, slip the wand into the end of a staff and it's like holding a pot over a flame.

An ideal staff would probably look a lot like the diagram below. The wand itself would be inserted into a glass or high-cone ceramic since these are the most heat resistant materials available in the middle ages. The holster would then be held by a steel head, preferably with seamingly decorative spines loops or other patterns to help it dissipate heat. Then the head would tapper back, thick to thin. The steel closest to the head will get hottest so extra girth will help keep it from melting or warping when it reaches malleable temperatures, but the tapper makes sure that less heat can spread back through the shaft. Then the handle itself would be wooden. Since wood does not propagate heat well, this will further insulate you.

Your castle volcano problem is a bit ridiculous for which you will need a ridiculous staff (aka pike staff), that will put a great as possible distance between caster and wand. More importantly, you need what basically amounts to a ballistic shelter similar to what Davy Crockett crews often used. That much heat will be explosive, and you will be in the blast radius, but if you are protected by a bunker where you are physically underground, the blast will mostly pass over you. The pike staff will be destroyed, but the caster, ducking under the level of the ground and with a shelter to absorb most of the radiant heat might just survive the blast.

The solution to your magic wand problem is actually a staff... I love when one dumb trope is the right solution to another. Much like your chopsticks proposal, you are using a device to hold it away from you. The staff puts distance between your hand and the wand which is important when you dealing with limited insulating materials. While the heat of the wand is enough to cause 3rd degree burns, the head of the staff will heat up a lot at the end but much much less at the handle; so, slip the wand into the end of a staff and it's like holding a pot over a flame.

An ideal staff would probably look a lot like the diagram below. The wand itself would be inserted into a glass or high-cone ceramic since these are the most heat resistant materials available in the middle ages. The holster would then be held by a steel head, preferably with seamingly decorative spines loops or other patterns to help it dissipate heat. Then the head would taper back, thick to thin. The steel closest to the head will get hottest so extra girth will help keep it from melting or warping when it reaches malleable temperatures, but the taper makes sure that less heat can spread back through the shaft. The handle itself would be wooden; since wood does not propagate heat well, this will further insulate you.

Your castle volcano problem is a bit ridiculous for which you will need a ridiculous staff (aka pike staff), that will put a great as possible distance between caster and wand. More importantly, you need what basically amounts to a ballistic shelter similar to what Davy Crockett crews often used. That much heat will be explosive, and you will be in the blast radius, but if you are protected by a bunker where you are physically underground, the blast will mostly pass over you. The pike staff will be destroyed, but the caster, ducking under the level of the ground and with a shelter to absorb most of the radiant heat might just survive the blast.