As Strider says, you want layers. You get hot going up, but it's easy to get chilled on the way down. So you need to be able to adjust. And, as it's Yorkshire, the outer layer needs to be waterproof, breathable if you can manage it, and light, in case you are lucky and end up carrying it. Then something warm, like a fleece underneath, which again you may only need for part of the walk.
I was lucky, the only time I did the Y3P it was warm, not too hot, and sunny. But days like that in the Dales can be rare, even in June!