It has been rumoured in the past that many D cells are in fact C cells inside a larger package. No idea about the truth of that.

All cells, when charging or discharging, have a chemical reaction going on inside them, which is always exothermic, i.e.. heat is given off. As a general rule, the more current, the more heat. To avoid overheating, the cells have to pass this heat to the outside world. The more surface area, the better the transfer. C cells have more surface area, they handle it better. High capacity AA cells have a very large surface area of electrode packed into a very small volume, when they operate at high currents, the heat is even harder to get rid of. If they can't keep their temperature within limits, they vent gas. This is usually water vapour from their store of electrolyte. When that reduces, it stops being a battery and starts being ballast.

If the use to which they are being put is within what they can stand, they will work and survive and be OK. Otherwise, to put a lot of ability into a small volume and at low weight, the answer is to go with Lithium.