Yes, if it shifted the axis 10 inches closer to the sun, things are most absolutely going to be warming up.
The Erath also spins, and travels around the Sun, so at times, what was nearest the Sun, is farthest away.
Well since it is the axis and not the whole earth that means while it basically increased it’s title towards the sun, that means the other end got tilted further away. Therefore it all balances out. Or at least that would make sense to me. But I got woken early today so my mind is mush.