I think you need to look at the whole circuit resistance, not only that of the lead. I do know Ohm’s Law. Do remember that the lead conductors are insulated – thermally, as well as electrically. I^2 will not halve, and the the resistance of the circuit will not double, but the resistance of the flex conductors will mean more thermal conversion in the lead. Do remember that Newton’s Law of cooling only holds for force cooled objects. Think about it a little.
I used to show a video clip of an electric fire, with a too small flex attached, to GCSE students. I hoped it was sufficiently dramatic to demonstrate that leads with too small conductors were not safe and that fuses wrre fitted to protect the flex, not the electrical item (no, necessarily, the operator).
So that makes two of you that think that using too-small flex wires will limit the current to the load sifficiently to avoid a fire? Perhaps you needed to join my GCSE classes of twenty years ago.