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To preface, my creatures have 4 horns, and they behave very similar to rams (at least ancestrally) in that they headbutt to resolve conflict/create dominance hierarchies. Two smaller horns are above their brows, and the other two larger ones are placed on the back of the head. I assume the best arrangement would involve increased surface area in the form of curling and ridged horns, but horns that still form a cage around the head, like dual ram horns.

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Curling the horns won't help any more then having straight horns would. The horn would still need to radiate from the base of the horn to the tips (via the horn) and curling them would reduce the airflow inside the curl as there is less space for it to travel. So Straight horns would help you radiate more heat, because you could essentially wave them around to increase airflow and the amount of heat you remove (like fanning yourself).

Essentially, as long as your horn remains a single solid round horn, the shape won't help much in reducing the heat. Instead, you want thicker or flatter horns which would increase the surface area more compared to the most efficient surface to area shape of a circle. This of course, would weaken the horns in certain directions as the forces wouldn't be uniformly distributed across the shape.

However, in terms of radiation, Horns aren't going to help much. They won't contain as many sensitive blood vessels to help distribute heat as skin would and their constant battering would damage any delicate blood vessels in them. Having smaller horns would be more beneficial as it would increase the surface area of your skin which would let you radiate more heat.

Aka, your Horns ( or our hairs ) are going to be better at insulating than radiating away heat.

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  • $\begingroup$ Yet mountain goats that live in very cold climates have small, straight horns. If big, curly horns helped with heat retention, why would mountain goats evolve this way and an animal like an impala (that lives in hot climates) have exactly the opposite type of horn? Not trying to insult you at all, I legitimately don't understand. $\endgroup$ – Tardigreat Oct 9 at 6:54
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    $\begingroup$ @Tardigreat Basically Horns do not help them lose or retain a significant amount of heat. Body hair has a far greater impact so the shape of your horns shouldn't be designed to be optimal for heat radiation. They should be optimal for bashing into other horns. Think of it like Finger or Toe nails. They might lose a bit of heat, but the rest of the skin on your finger is far more important in that aspect. $\endgroup$ – Shadowzee Oct 9 at 6:57
  • $\begingroup$ Perhaps not significant in some animals, but I've heard that goats rely at least somewhat on their horns for shedding heat; their horns feel noticeably warm to the touch and when goats are disbudded they are reported to have issues with heat regulation. $\endgroup$ – Tardigreat Oct 9 at 7:00
  • $\begingroup$ Besides that, I'd like to have the horns be at least ancestrally useful in fighting and retrofitted for thermoregulation, as my animal is large brained and would benefit greatly from heat radiators on the head. (Noting as well that this animal does not have mammalian ears nor any fleshy part of their face other than their lips and a turkey like 'snood' to fulfill this purpose) $\endgroup$ – Tardigreat Oct 9 at 7:10
  • $\begingroup$ @Tardigreat Being Warm to touch at room temperature indicates it is a poor heat regulator. The Material likely is a bad thermal conductor because it isn't transferring the heat around. Compare this with metals which will feel cold to touch at room temperature, because they are great heat conductors. $\endgroup$ – Shadowzee Oct 9 at 23:23
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You want antlers.

https://en.m.wikipedia.org/wiki/Antler

irish elk antlers

Antlers are specific to the deer family. Unlike horns, antlers are bone and so have blood flow thru them. This will allow heat transfer up from the body. Antlers also occur in ramified, spatulate shapes (like the Irish elk antlers depicted) with large surface areas to emit heat. Of course antlers are also weapons and used in heat butting contests against conspecifics, as well as to deter predators.

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  • $\begingroup$ Isn't that only during the velvet/growing stages of the antler. Once that stage is over and you have your traditional antler, it is effectively the same thing as a horn. It even falls off once the season is over. $\endgroup$ – Shadowzee Oct 9 at 4:06
  • $\begingroup$ What could you do to deter bruising during intraspecific fighting if the horns have a large supply of blood in them? I'm sure there is a way to have a happy middle between not damaging the blood vessels in regular collisions and still being able to radiate a sizable amount of heat. $\endgroup$ – Tardigreat Oct 9 at 7:07
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    $\begingroup$ @Tardigreat - do not deter bruising. This is fighting! If you are worried about getting bruised you should stick to composing love poems. If you fight and hit hard enough to break off a vascularized antler spike it will hurt and it will bleed and then it will stop. That does not mean you have lost the fight. $\endgroup$ – Willk Oct 9 at 14:37
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Different body functions are usually handled by different organs or structures. Heat radiation requires large surfaces, while horns and other weaponry requires strength and the ability to concentrate or dissipate force (concentrate for damage, dissipate for protection).

Elephants, for example, have large ears for heat dissipation and separate tusks for use as weapons Stegosaurus had heat dissipating fins on the back and protected itself using spikes on the tail

enter image description here

Reconstruction of two Stegosaurus species

So the creature is most likely going to evolve a separate structure for dealing with heat, either external radiator surfaces or possibly some sort of internal mechanism like the air spaces in birds to radiate and dump heat into. A more exotic alien biology might have evolved something like a heat sink, requiring the creature to retire to a safe place after exertion to allow heat to flow out of the heat sink organ, or perhaps might carry some sort of expendable coolant, drinking a large amount of water prior to exertion and ejecting the hot water afterwards (sweating is not an exact analogy of how humans do this, but it is possible to amplify the idea, perhaps the creature spits or urinates the hot fluid).

Look at how this is done in nature for ideas.

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