I just love how the words 'cool' and 'colder' are used - making those verses magical.
I'm pleased you agree.
In fact I like the way most of the song holds together by the idea of healing someone. "I'll make it better' is what you say to a child who needs comforting maybe because he has just hurt himself. But the song goes beyond physical pain.It's both mental and physical.And for once I think maybe Lennon was right when he said it was partly aimed at him and his relationship with Yoko.
It's almost as if falling in love is a kind of illness which can only be cured by giving in to it. The girl in question is an antidote to the pain. Everything will be OK if you let the antidote under your skin and into your heart, but to do so you have to acknowledge you're human and can't always be responsible for everything and everyone out there in the world.
The song of course came out in 1968 when revolution was in the air. On the B side of the single Lennon sings 'We all want to change the world' but on the A side McCartney sings 'The movement you need is on your shoulder'. That's to say, it's not a political movement that will heal you but a physical, loving relationship.
Incidentally I've just noticed in the middle of Paul's song is something that obviously inspired John : Hey Jude don't let me down