First lets abuse the system as much as possible.
I'm sure you heard the good old saying: if you send your soldiers to a fair fight you are a bad general. Or something like that.
Well. The first objective for all generals is to abuse the system, like you do in a video game, to gain the most out of it. Because this is how warfare works. You bring overwhelming power into even the smallest engagements. As far as the military is concerned there is no such a thing as overkill.
Anyway I just link to demonstrate the theory and get into actual practices.
Now I will assume you want a tuned down magical system that has limits. For example both the initial and latent heating can only be used so much before the soldier simply burns up. And I will assume that the traditional method, basic stuff without help, does not accomplish insane spells or crazy stuff. Because if it does then we have to know exactly the conversion rate or the details.
Anyway you say they heat up. Well. We can transfer heat. Right?
Instead of bothering with "magically" making the heat go away and trying to break the laws of thermodynamics.
Why not take a page out of our actual science and just transfer the heat?
For example the CPU in the device you are using to view this, I will use PC as example but the same thing goes for all others, gets hotter with usage.
But you get a little fan, I know liquid cooling exists but lets simplify things now, that works as follow quote: "Simply put, a heat sink is an object that disperses heat from another object. ... The heat sink has a thermal conductor that carries heat away from the CPU into fins that provide a large surface area for the heat to dissipate throughout the rest of the computer, thus cooling both the heat sink and processor."
Lets copy that.
Be it pieces of meat, dead animals, living animals, complicated shields with layers of materials, or a wizard connection all soldiers into a grid and then heating up the actual ground, water to boil it, food to cook...etc.
So here is it how it works. Spells are a double effect. They accomplish effect A, speed or sight or whatever, AND object B which is transferring heat from the soldier to the ground, again just an example.
I don't see this breaking anything as you have simply let a way for heat to follow thus the soldier can draw on more and more power while still being cooled not by magic but by the fact that heat is going somewhere else.
Yes there still limitation here. I mean it's your world so I imagine you will provide them as I have no clue.
But this system will allow increased power not breaking the system.
For example you might have made the system that a move a mountain spell is theoretical possible however even the initial heat is too high that the person is incinerated before they even finish the spell.
But this allows the normal person say to move 2 bottles of milk magically instead of just one. Just an example.
Magical management officers. MM officers for short.
Why? Because this is how the military works.
MM officers are outside the chain of command, and subject only to their own regulation and officers.
MM officers sole purpose is to make sure that soldiers do not use too much power or heat themselves too much and so on.
The general, overall commander of the campaign, can't let his own soldiers just use whatever they feel like is appropriate and he also can't prevent them from doing magic, I only read from the link the part about magic being so widespread, so a comprise is needed.
You can add all sorts of things to them. They would powerful wizards themselves but more important they should be able to detect magic and overuse or under-use of magic.
Imagine platoon Delta has 44 soldiers. 43 soldiers cast increased speed while an A-hole soldier forgot to do so. That soldier is a weakness.
Now maybe for platoon Delta it is not a problem. But multiply that by say a 100 similar incidents on the battlefield and your plan and formation is doomed.
Overuse is also as bad as under-use. Say Craig is a brave soldier who casts bravery on himself and then rushes to meet the enemy. His bodies Matt and Tony run off after the idiot to bring him back and your shield wall is gone.
Again multiply that by a 100 and you can see the issue.
Magic is only practiced by orders
Makes sense. Much like you don't move an inch without orders this solution means that after the general gives the command of X then it is carried out.
But it is up for individual officers to interpret this command, at least on the magical level, and use the appropriate spell to achieve the goal.
This would, I think, advance warfare theory to Clausewitz style where the general sets the overall goal and those below him go about adapting to the changing battlefield and choosing the most appropriate approach.
Officers training and teaching would become more vital.
The larger more established states with academies and large institutes would do better as they can afford to train their soldiers on the officers level on how to be actual officers not just someone shouting stuff and charging the enemy line while saying cheesy stuff like: do you want to live forever.
However actual warfare is messy so expect exceptions.
- Strength would only be used for archers oddly enough. Regular infantry won't benefit much from raw strength.
- Because of that earlier point we could see more archers as a result of the fact that archery requires years and years of training. But if you can simply magic strength and accuracy then we might see way more archers.
- Stamina magic and anti exhaustion magic would the most useful one. As we all know war is like 95% marching, 4% maneuvering, and 1% fighting. OK I made that up but you get the point. The ability for a general to force march his soldier beyond the human point is a 100% game changer. So many of Caesar's, because I read on him,
victories are a result of one simply trick. Forced marching. Sun Zu himself is all about that stuff. Surprise marches to materialize where you are not excepted wins battles more that numbers or technology. So extending the ability for soldier to just march is a game changer of the highest level.
- Speed magic. For the regular infantry reaction time is far more valuable to strength. The enemy would be clad in armor and using shields. But the ability to swipe away that spear point or deflect that sword cut is the actual difference between life and death. Now in tight formation things are not as loose, does it count as a pun?, but still the ability to be faster is more important than strength.
- Scouting just became a lot easier.
- Ambushes now are almost obsolete. I mean don't get me wrong. There is always an idiot who will march through a dark German forest without using a single detection spell, Varus where the heck are my legions?, but most of the time that just becomes not a thing.
- Does war become more deadly? Maybe. I mean in reality what causes the most casualties is the route not the battle itself. However if you have to sides with such high moral, magically boosted, then booth sides annihilate themselves. Pyrrhic victory every time.
- So you can have all wars become wars of attrition or you can have sensible generals who would issue retreat orders when they see the military need. You can enforce that with magic, MM officers, banning courage spells, actual battlefield punishments...etc. As Clausewitz says: "In War the Result Is Never Final
Lastly, even the ultimate outcome of a war is not always to be
regarded as final. The defeated state often considers the outcome
merely as a transitory evil, for which a remedy may still be found in
political conditions at some later date. It is obvious how this, too, can
slacken tension and reduce the vigour of the effort." so your actual general should be aware of that and not throw the lives of their mind to satisfy their ego.
- Visibility spell are worth their weight in gold. The amount of battles decided by poor visibility would keep me righting for a day. So the ability to see clearly is just so important that it would change history.
- Hunger and thirst spells are also important. There will always be times when your are fighting on an empty belly or waiting for supplies. If your magic can include actually sustaining people then this is an absolute game changer. Supply lines don't become a thing as much. And this changes many many things.
- Cavalry perhaps would fall out of use. Because of the difficulty of heating and how the animals would suffer or prevent you from doing much magic. Also remember than cavalry are more vulnerable to attacks, even cataphracts and full plated knights, and all you need to do so stop the mightiest cavalry charge is whip out lots of large powerful longbows. Or just equip your soldier with throwing spears and increase the strength of their arms.
That's all I could think of for know. If you know more about the magic system and the limits I'm sure we can help you further.