Let's separate out the emotion part of it. Emotions might be needed to cause the effect in your world, but basically you are asking about the energy needed for a human to be able to effect the world with just their mind--which is in most systems called magic.
Currently we cannot achieve this particular effect and neither can any animal on earth.
As to tech controlling it, we also don't exactly have any models which can control weather, so it's difficult to use science as a basis. The U.S. air force apparently has something that can but this takes triangulation. See too this wikipedia article on weather control. As you can see, the models we do have are tenuously science-based.
Heating the air will cause a change in pressure locally, but the question is really, how many degrees will it need to be changed in order to cause any noticeable effect?
Temperature and pressure are directly proportional
to each other. This means that as the temperature
decreases, the pressure also decreases, and as the
temperature increases, the pressure increases. One
way to think of this is if you increase the speed of the
molecules –by increasing their temperature- the
force of the molecules hitting their container
increases and this increases the pressure. This
relationship is called Gay-Lussac’s Law and makes up part of the ideal gas law.
When the speed of a gas’s molecules increases, the gas molecules hit their container more often. The
more frequently the gas impacts the container walls, the higher the pressure. So, as temperature increases,
the pressure also increases. If the gas cools, the impacts are less frequent and the pressure decreases.
This relationship can be described using mathematics as well. Mathematically, Gay-Lussac’s Law states
T = k
I have been unable to find any equations that determine the exact difference in temperature needed to cause a localized effect like the one you are talking about. However, the amount of energy needed to agitate air molecules to cause this would be high.
Think of it this way--your house might be heated 20 degrees higher than the outdoors, but when you open the door to the cold, how much wind is created? Anything? A small effect? Until we know how much the temperature has to rize, and indeed, how the person in question is supposed to keep it localized without losing heat to the environment around them, this is a difficult question to answer.
But, to start you off, if you are using science, look at the laws of thermodynamics. Energy cannot be created or destroyed. It has to come from somewhere, so your humans must have a power source within them--something that can be quickly converted to output the massive amount of energy you are talking about.
So the very first thing your human will need is a power source. We do have one animal which does convert things to electricity. The electric eel.
The electric eel has three pairs of abdominal organs that produce electricity: the main organ, the Hunter's organ, and the Sach's organ. These organs make up four-fifths of its body, and give the electric eel the ability to generate two types of electric organ discharges: low voltage and high voltage. These organs are made of electrocytes, lined up so a current of ions can flow through them and stacked so each one adds to a potential difference.
If you are looking for an evolutionary push, I would look to the electric eel and why it developed this ability. To hunt prey and for defense, basically. Notice though that this isn't anywhere NEAR the energy output of what you would need to get your effect, but it is a place to start. Your humans would have to have had an advantage and efficient system/organs to use this ability. That likely means tougher predators and prey, as well as, perhaps animals in this biosphere that can achieve similar effects of energy conversion. (It's likely, but look at the eel, which is an outlier and unique).
That's about as scientific as I can make it. Hopefully other posters can determine the amount of energy needed for such an effect.