There are three main causes for heat build up in a coil of wire carrying an AC current. The first is the heating effect of the current passing acting on the ever present resistance in a conductor. The second is the the effect of the power factor of AC appliances, and the Third is the induction effect, which is usually related to high frequency electrical systems.
The induction effects are miniscule at normal mains frequency so for this purpose can be ignored.
The Power factor is consideration where there are large electric motors and a lot of old style fluorescent lighting more of an industrial problem than a caravan, so again this can effectively be ignored in this instance.
As most caravans present a majority resistive load, we can use simple Ohms law heating calculations.
Every electrical cable has some resistance. Resistance opposes the passage of a current, and in doing so the lost current is released as heat. The standard EHU cable has conductors of 2.5csa will have a resistive value of about 0.007Ohms per meter for each conductor.
From:
http://www.nktcables.com/dk/products/railway/railway/technical-information/~/media/Files/NktCables/Products/UK/Railway/technical%20info/Copper-wire-table.ashx
Because the same current flows in both Live and Neutral conductors you have to double the value to 0.014Ohm per meter of EHU cable. The earth conductor should not have any current flowing, so it will not produce heat.
As we are have Current and resistance, Ohms law tells the energy (heat) is the calculated by the Current squared times the resistance. If the cable was carrying its full rated current of 16A then we would get heat losses of 16A x 16A x 0.014Ohms = 3.584Watts per Meter
For a full 25M EHU that would be 89.6W. Do you remember how hot a 40W light bulb got well this is two and a bit light bulbs of heat. If this was tightly coiled you can imagine how hot it can get. But that is if it is carrying the full 16A, which most of the time it won't be.
The kinks in a cable can start to produce problems if the conductors have been constantly stressed they can start to stretch and loose csa which raises the resistance at that point. This can lead to a hot spot in the cable as well as the damage to the insulation mentioned by others.
The standard EHU cable uses PVC on PVC insulation and will be rated for a maximum surface temperature of 70C. BUT If a cable self heats and is produces 70C surface surface temperature, it must be significantly hotter inside, and that will be enough to deform the insulation and reduce its effectiveness, rendering dangers of electric shock as the insulation may have thinned.
I would prefer to see the coil in the picture spread out a bit more so it is better able to lose heat more effectively. The kinks should also be avoided to prolong the life of the EHU.
The advice about uncoiling cables is principally aimed at cables that are tightly coiled on a drum or more particularly in an enclosed drum, where there is little means to let the heat escape which can cause a temperature build up. This can start a cascade reaction because as copper heats up its resistance increases, which means for any given current more energy will be lost in the cable generating even more heat. The corollary of this is as the resistance rises less current will pass for a given supply voltage, but that is not an excuse to leave power cables tightly coiled when in use.