I wouldn't worry about fungus gnats eggs in compost. They exist in the environment anyway, and there are no doubt things that eat them to keep their numbers in check. And a hot compost in particular should do most of them in. They become a problem when starting cutting indoors in a previously pseudo-sterile environment. I had horrible fungus gnats two years ago, and many of my cuttings survived in spite of them, and then once they got outside, there is no more problem.
Now, I wouldn't use said compost for starting cuttings indoors. Then you're just asking for trouble. Even a handful of eggs surviving can start an infestation indoors. If you must do it, then yes, please sterilize in the microwave first. That sounds pretty nasty to me, but should get the job done.