I'm in the middle of a dry spell, a "burnout"... I want to write, but I can't. Miss Muse has hidden herself away somewhere...
This sounds more like writer's block than true burnout. With burnout, you don't want to write, you don't want to read, you don't want to do any of the things that you've been doing. The answer there is to STOP, and let yourself go away for awhile. Forcing yourself past true burnout is going to lead to someplace much worse.
If you WANT to write but can't--which sounds like writer's block--then shift your paradigm. Go read a book in a completely different genre. Give yourself a flash fiction writing exercise about a subject you've never considered before. Give yourself permission to play, to write terribly, to have some FUN. At the end of the day, isn't writing supposed to be enjoyable? Why else do we do it?
Above all, CHANGE something in your mental state to release the log-jam in your creativity. Don't begrudge yourself a day doing something different. BIC is mandatory but ya gotta know the difference between discipline and torture. The muse won't be lured back by you sitting there sweating blood.
What's more wasteful: staring at your monitor writing nothing (or garbage) for days on end, or giving yourself the gift of some time off (even an afternoon) doing something to jostle your creativity?
You'll probably find that 'wasted' day will pay you back beyond your (and your WIP's) wildest dreams in productivity and fresh ideas.