stick out the window

Here is the situation.

I am smoking a cigarette outside my window. My friend asks me if I'm cold. I'm sticking my head out the window so that the smoke doesn't come in.

I say

The only part of my body that's cold is the part sticking out the window.

Which is correct?

AThe only part of my body that's cold is the part sticking out the window.
BThe only part of my body that's cold is the part that sticks out the window.
C Different tense

If someone says:

I am smoking a cigarette outside my window.
I'm sticking my head out the window smoking.

Is that correct and natural? Could you correct the 2 sentences please?

Thanks