Skin effect with superimposed frequencies
Short answer
no. Skin Effect is fully explained by the linear model of Maxwell's equation, so different frequencies can be considered independently.
Also
at 50 Hz, your skin depth is about 9mm; far thicker than your conductor is (makes sense, right? Otherwise we wouldn't be using massive copper for power distribution!).
Long answer
Skin depth being non-zero is due to non-ideality of your conductor. Of course, if you heat up a metal, it changes conductivity / resistance.
In your case, 6mm² carrying a maximum sum current of 35 A: Ignore. Your cable has about 2.4 mΩ resistance per 1m of length; P=I²·R~=10³ A² · 2.4·10⁻³ Ω = 2.4 W. Getting rid of 2.4 W of heat over 1 m of length: will happen by itself.
With the three currents at the right frequencies, we can even be specific:

5A @ 0 Hz: &quot;infinite&quot; skin depth. No significant heating due to this current.
15 A @ 50 Hz: skin depth &gt;&gt; radius. No significant heating due to this current.
15 @ 15 kHz: skin depth ca 0.5mm. Resulting area of conducting cross section is \$\pi\$·(outer diameter² - (outer diameter-skin depth)²)=\$\pi\$·(0.78² - 0.28²) ~= 6mm² - 0.88mm² ~= 5mm². No significant heating through this current.

Things get worse in nonlinear materials, but I'm pretty optimistic that your copper conductor is linear enough.