Question

why the south Pole of earth is always cold and the north pole is hot at any angle

Answer 1

It is only because only because of the Sun

Answer 2

Both North Pole (the Arctic) and South Pole (the Antarctic) are cold because they don't get any direct sunlight.

The Sun is always low on the horizon, even in the middle of summer.

In winter, the Sun is so far below the horizon that it doesn't come up at all for months at a time.