In most fantasy stories elemental fire magic is used either as a substitute for guns in warfare, but in a modern setting how would the military use fire elementals?
Fire
Modern militaries depend on things which go boom. They have to store those somewhere. Generally, the place you store ammunition is called a magazine or ammo compartment.
If the enemy can magically introduce the force of fire into your magazines at will, he can "cook off" your ammo inside your vehicles. Any fighting vehicle is finished (except a few modern tanks designed to survive that). No aircraft can survive a carried bomb detonating (it may be able to eject a missile engine firing on the rail). A magazine fire on-ship becomes a "save your ship" emergency; the larger ones can flood their magazines with seawater. They certainly they won't be doing any fighting at that point.
So a fire-manipulator who really knows what he's doing, can take all the fight out of a modern military. If anything it creates an interesting opportunity for a relatively nonviolent way to end a war.
"The ability to control fire" and "modern military" are entirely exclusive. The two cannot exist together.
What is a modern military if not controlled fire. Fire in the breach, fire in the hole, burning jet fuel, engine fuel.
To control fire implies also to suppress fire, fire suppression over an area turns a modern military into a bunch of guys with expensive scrap metal. Guns won't fire, engines won't run, planes fall out of the sky, bombs and missiles won't explode, it's all ultimately fire.
Even if you don't allow fire suppression, aircraft that explode with a wave of the hand or the ability to detonate an ammo dump with a thought, equally shuts out any modern military capabilities.
To answer the question: I'd say the ability would be something like dropping napalm from a plane, without a plane. It would also be nice for cooking and warming up the campsite, I guess. It could allow a single wizard to stop an oncoming charge, defeat a cavalry charge or beach landing. Burn a village to the ground from atop a hill or tree. It might offer a unique escape: let the wizard climb a tree in the forest, and then burn everything around him (but not his own tree) to kill or drive off soldiers pursuing him in the forest.
ELECTRICAL: Both the brain and heart are absolutely dependent upon finely controlled electrical impulses; which are typically self-regulating. This is why a defibrillator works; the shock forces a new electrical state which a heart can self-regulate back into a normal rhythm. Control of electricity allows a wizard to cause anything from instant unconsciousness, epileptic-like seizures, heart attacks or just instant death, by disrupting or overloading biological electric impulses. Also, of course, disrupting or destroying any electrical device, just like lightning can, and (like an electric arc welder) it might be used to melt or deform metal.
PLASMA: not very useful, but hot enough to burn through metal and stone, perhaps.
can I be frank for a moment? I don't think you know much about the world we live in and what plasma, fire or electricity is. I recommend getting some high school level book about physics and reading a bit and then comming back to ask questions. Please double check plasma because I think you just read that word once and now want to write a book about it.
Controlling a fire sounds like you are able to control the shape of the flame. Please understand how unspecific your question is. Here is my best guess though:
Being able to control the shape of a flame as no applications in contemporary military since scorched earth tactics and other barbaric strategies are no longer used most of the time. The only way that would be useful that I can think of is to start large wildfires - which is already pretty easy.
Controlling the heat sounds a bit more useful. So how fast is this working? If you can melt an aircraft carrier within a couple of milliseconds, this would solve almost all problems the human race is facing right now. If you need a day to make scrambled eggs - nobody cares. Is this once again about deciding in which direction heat flows? This would certainly have industrial applications, maybe in weapon manufacturing? The interpretations and applications of this one could fill books.
Controlling electricity is the most vague one yet. Even if you can rain down lightning on enemy armies, this would a) once again be barbaric and not really done by any serious military and b) pretty useless in most modern battlefields, e.g. cities for example and finally c) so powerful with so many applications that our world would be completely different. If you can control the way currents flow - well, a normal human isn't nearly fast enough for this. Please check out how fast electrical signals are transmitted.
Creating small amounts of plasma sounds a bit like digestive problems. Please be more specific and read what plasma is and how this is already included in 1), 2) and 3).
Oh, and another note: Of course most warfare is still barbaric, but a lot of this has to do with how much money all those tools cost. If you get the same result for free, we would see a lot less of barbaric behaviour. Be aware that a lot of warfare is because of economic reasons.
