why would you keep it in an open container, and in the furnace room? i did my cleaning in the garage, or outside when the weather was decent.
if you want to prevent rust, you'll need to avoid using water OR use some follow-up stuff to fully displace the water (even in the pores of the metal), like maybe WD40. kerosene is a great cheap solvent that's probably more stable than gasoline and won't cause rust. to dissolve dirt and grime, you kinda have to use a solvent of some kind, and most are gonna be flammable one way or another. kerosene just happens to be one of the cheapest and most readily available ones - and it's safe on blued or park'd parts (i know from doing my Norc that way)
you COULD do the cleaning in water, but then be sure to follow up with a bath of some kind to get rid of the water. or pop the parts into an over to dry them out, perhaps. of course, water will very likely leave mineral spots when it dries, so you may have to clean THOSE off as well.
FYI - i keep a 9L jug of kerosene in the garage, and used it to clean every single part of my Norc (except the grips), and my motorbike chassis / chain, and all my hand tools, and... and... and... been using it for all sorts of cleaning for 10 years. never had it catch fire unless i actually used it to fill up a lamp with wick and put a match to it.