first, a low intensity, 5 min warmup is not a bad idea
then HIIT
how much muscle do you think you're going to loose in 20 minutes? Not much and for the first few minutes you'll be burning up lingering glucose/glycogen, depends on your cut off time for carbs, if you ate any.
a 20 min cooldown can be used to burn additional fat, then you want to eat some fat and protein,
You know insulin inhibits lipolysis!, so not a good idea if fat loss is the game, why not save the carbohydrates for before / after weights or sports, but really this all depends on how active you are throughout the day.