Another song about wanting to change places with someone else:
The underlying conceit is the same as that in Nik Kershaw's Wouldn't It Be Good: intensities (freezing/burning) are exchangeable, substitutable. "Running up that Hill" is about the ascent towards ecstasy, a troubled and turbulent ascent ("there is thunder in our hearts") which Bush imagines could be made smooth and easy ("be running up that hill / with no trouble") if only a deal could be struck which would render the lovers interchangeable, each having direct knowledge of the other's tribulations ("don't you want to know that it doesn't hurt me?").
The problem in both cases is one of empathy. Kershaw's lyric personae get into a kind of contest about who's got it worse ("I'd stay right there if I were you") while the song (from the position of Bush's "God") withholds from both the knowledge that they're in the same existential fix. Bush embraces intensity, without desiring to escape from it, but wants to know how it can be converted into an upward spiral of mutual fulfilment. At the same time, the song itself seems to enjoy its own swirling languor, punctuated by occasional lightning-flashes within the clouds. In spite of the underlying rhythmic pulse, it's not actually in a hurry to go anywhere in particular.
When I was a child, songs like this always raised the troubling and unresolvable question: is she singing about sex here? The answer is fairly obviously "yes, and...", but it's determining where the "sex" stops and the "and" begins that's difficult (perhaps the sex never does stop: when is Kate Bush ever not singing about sex?). Dramatic and troubling, this song always seemed to me to present an aspect of grown-upness that I wasn't sure I'd ever quite be ready for. I'm not altogether sure I've got the hang of it even now.