The answers provided so far are a little light on the actual mechanics that warrant balancing on Lithium chemistries and not on others.
First of all; all battery chemistries benefit greatly from proper balancing. Balancers are used on spacecraft nickel cadmium batteries, certain types of (low discharge) lead acid batteries and so on. All battery chemistries are just a certain dominant chemical reduction-oxidation reaction which occurs between certain Gibbs energies (or Redox potentials if you take into account both the anode and cathode reactions) - hence between a certain lower and higher voltage level. Above or below this 'ideal' range of voltages, other reactions may occur - or otherwise minority reactions become dominant.
These other reactions often are not reversible, hence they reduce the amount of 'useful' anode and cathode material, reducing capacity. Sometimes such unwanted reactions are even more dramatic, creating compounds that corrode the electrodes, degrade the electrolyte or cause toxic/explosive chemicals to form.
Now, these dangerous reactions are the primary reason why lithium chemistries really require safety circuits. Both when overcharging and overdischarging, depending on the electrolyte used, an explosive gas mixture is formed. More importantly, when the anode becomes too hot (about 125C), an exothermic reaction starts which accelerates itself, consuming most of the energy stored in the battery (thermal runaway). This is often caused by self-heating when dealing with large discharge currents, or with unwanted reactions caused by overcharging. As lithium chemistry batteries have energy densities up to more than an order of magnitude more than nickel and lead chemistries, i.e. a lot of energy in a small place, this can cause a big boom. Especially when combined with an explosive hydrogen-oxygen atmosphere.
Other chemistries have the same problem, though! Wet-cell Lead acid batteries are very well-known for producing hydrogen gas, even in 'normal' use, but mostly when abusing the cells. Lead acid cells can also go into thermal runaway when the sulphuric acid is concentrated enough. However, because of the relatively low energy density and high thermal capacity of the plates, as well as the high temperature at which thermal runaway kicks in compared to lithium ion, this is not a risk that needs to be dealt with in most situations. And the same goes for nickel chemistries, which often come with balancers in high-current applications (e.g. RC cars) - or your battery will only last 10-50 charges.
Then there's the practical question: can you just put lots of cells in series and pretend it's one big high voltage cell? Yes, you can, but the battery lifetime will be horrible. Any cell mismatch in your 12-cell stack will be exacerbated each charge-discharge cycle, and after a couple tens or maybe 100 charge cycles you will have a dead battery. It may even cause a safety hazard. So both for your safety and optimal use of the batteries it is very strongly recommended to use balanced charge management.
So I did some research and found out that there's a recent advance in battery technology that allows LiPo cells, used in both mobile devices and hobbyist/RC applications, to operate at higher voltages. Specifically, a silicon-graphene additive is used in the anode to protect against corrosion at higher voltages, allowing them to be charged to 4.35V or even 4.4V. This results in slightly higher energy density, but charging the battery to higher voltages can reduce its service life.
The high power consumption of mobile devices means that high energy density is more important than any other characteristic. This means that reduced service life is an acceptable trade-off; since the typical consumer replaces their smartphone every two years, service life is not a major requirement.
In essence, the higher voltage is just another avenue of increasing overall energy density.
Best Answer
I did not do any calculation at all, but I am pretty sure that a Lixx battery would not last long enough to heat.
The point is this: batteries stores electric energy, that is a quite high level energy. You can use it to run computers, power engines, lights, and to heat things. But batteries have a quite low specific energy.
Rechargeable lithium batteries are under 1 MJ/kg while oil is as high as 46 MJ/kg. This means that oil can provide a lot of energy more.
If you'd want to power an electronic device a battery would probably be a good idea, with oil you'd need a generator, but you want to generate heat. Heat is the lowest quality kind of energy, converting anything in heat is very very simple and above all is very efficient. For oil, you burn it. For electrons, you squeeze them through a resistor.
To answer your questions:
You might want to search for propane burners, I bet there's plenty of electronically adjustable burners. To change directions you might want to install some small propellers on your hot air balloon basket, and yes, these might be powered by a battery.