- the thermal resistance of the ambient where the cable should work (of course air for me)
I'm afraid it's not that simple.
You have a conductor inside that is being heated by the current passing through it, we express this as power per unit of length (W/m).
You then need to take into account the thermal resistance of the insulation, you know the inner and outer diameter of the insulation, the specific thermal resistance is probably expressed in the cable's datasheet, one simple integral and you have the thermal resistance per unit lenght (K/(W*m)). Everything is clear so far.
This is where it gets tricky - the cable dissipates the heat in two ways:
-convection (heating the air around it)
-radiation (by radiating in the infrared spectrum)
Convection (Newton's law of cooling):

Let's simplify this.
The differential of heat over time is power. Let's assume a constant temperature of the surface of the cable, so we can drop the function of time.
What we have now is:
P = h * A * (T
cable - T
ambient) (power = heat transfer coefficient * surface area * temperature difference)
Let's divide it by lenght.
P/l = h * C * (T
cable - T
ambient) (power per unit length = heat transfer coefficient * circumference * temperature difference)
Let's say we know both temperatures and the outer diameter of the insulation. We are lacking one crucial piece of information: heat transfer coefficient. It depends on many, many variables. You could probably write a dissertation on that topic.
Radiation (Stefan's law) (in case you didn't know, Jožef Stefan was also Slovenian; just wanted to point it out

):

There is an asterisk next to the j, because we also need to take into account the
emissivity of the surface. A black body (completely absorbant) would have the emissivity of 1, while a white body (completely reflective) would have an emissivity of 0. Our cable's insulation would have an emissivity somewhere between 0 and 1.
Let's rewrite this a bit:
J = sigma * T
cable4 * epsilon
P/A = sigma * T
cable4 * epsilon
P/l = sigma * T
cable4 * epsilon * C (power per unit length = Stefan's constant * (Temperature of cable)
4 * emissivity * outer circumference)
So here we have the equation to calculate the power dissipated through infrared radiation. The problem is we don't know the emissivity of the insulation. You certainly won't find it in the datasheet.
And there is also one more problem: The same way the insulation radiates the heat, it also absorbs the radiated heat from the surrounding components. Try to write an equation for that!
If we managed to find all of the unknown coefficients, we would need to cram in all into a single bulky equation and calculate the temperatures of the different parts (conductor, insulation surface, etc.) and make sure that they doesn't exceed the maximum rating (with a safety margin, of course). There's an idea for your second dissertation.
Oh, and let's not forget that when the cable would heat up, the conductor's resistance would change, and all of your calculations would go to hell.

As you probably figured out already, calculating that in theory would be pretty damn difficult. You would be much better off just using the tables and picking slightly thicker wire gauges, just to be sure.
