Induction plays no role whatsoever in this. First, as already pointed out by @Jerther, the hot and neutral cancel off. It doesn't matter whether twisted or not, it's still a bifilar winding with negligible inductance.
Now even if the coiled extension had inductance and thus presented reactance (not resistance) that causes voltage drop for AC current, the energy "consumed" on that perceived voltage drop is not turned into heat, but rather temporarily stored into the magnetic field and returned out of phase of the AC current.
Still, coiling is bad and leads to higher temperature (and higher losses caused by warmer copper), because it keeps the power loss concentrated in smaller space, when the heat can't radiate out as easily.
Now even if the coiled extension had inductance and thus presented reactance (not resistance) that causes voltage drop for AC current, the energy "consumed" on that perceived voltage drop is not turned into heat, but rather temporarily stored into the magnetic field and returned out of phase of the AC current.
Still, coiling is bad and leads to higher temperature (and higher losses caused by warmer copper), because it keeps the power loss concentrated in smaller space, when the heat can't radiate out as easily.