Gosh, this Seventh Doctor novel is pretty poor. Lots of good ideas, including William Blake, disappearing planets, Cthulhoid monstrosities and the secret history of Rassilon, but thrown together really hastily so that the reader must find some real motivation to make sense of it all, and I could not find that motivation.
From the Heart of Europe
Books, politics, languages and life
Depends if “desert” = “hot”. If not – and strictly the definition of desert is dry, not hot (there’s a desert in Antarctica – indeed IIRC it vies with the Atacama for driest place on the planet) – then it’s perhaps not entirely implausible to have all the water locked up as ice. But if this is the usual “desert = hot sandy place” then, no.