Good question. Think it through.
At first blush it seems to me that the biggest risk is fire. So I tried to find the flash point for smokeless powder. Wiki is a failure, it says the flash point is 37 degrees F. Since I have some stored at 75 F and it isn't on fire, I'm thinking that we do not share a common meaning for "flash point". Next I looked up "autoignition temperature" - I found them in the Materials Safety Data Sheets from several powder manufacturers. These seem to range from about 160 C to 200 C or about 320 F to 392 F.
If you can touch every external part of your furnace with your bare hands then the exposed part is less than about 140 F and the furnace should not ignite powder. What about the flue? That's hot, right? Maybe. Depends on the gas furnace. I had one where the flue temperature was less than 100 degrees, we used white plumbing pipe for the flue. If you can imagine a scenario where smokeless powder could come into contact with a hot flue or something else hot on your furnace then move your bench. Otherwise, so far you are good.
Forced air furnaces move a lot of air and they warm it up. If the powder is in the air, how far will it go - can it get sucked into a hot place? Are there holes that powder can get through and come in contact with hot stuff? Are you messy and have powder all over the floor or bench? Can you get airborne powder in contact with your furnace or flue? Are you using stick or ball powder (each piece is fairly heavy) or flake powder (each piece is really light and might float in the air)? If any of those had the wrong answer, you need to load somewhere else.
Next issue: liquids and vapors. If you use a volatile liquid on your bench, maybe a cleaning solvent, maybe the liquid will evaporate and create an explosive fuel-air mixture. Ignited by the furnace you would launch yourself (or parts thereof) into low earth orbit. Although it sounds like fun, your insurance rates would go up, it will make a mess that your wife will want you to clean up, you will be in no position (or perhaps many positions) to oblige, so you should probably avoid it. In some cases especially if warm powder breaks down and one or more of the decomposition products makes a flammable vapor. Sometimes during the manufacturing process powder is cleaned or extracted using ether or acetone - both flammable. I would not worry too much about powder products but if I thought about it, I probably wouldn't clean guns with gasoline in that room.
Powder should be stored in "a cool and dry area". Furnace rooms are not one of those. Elevated temperatures will accelerate decomposition. If you load in this room, store your powder and loaded ammo somewhere else.
I once had a 10x20 reloading room that contained a propane forced air furnace. I loaded a lot of ammo in there and cleaned a lot of guns. It never struck me as a death trap - there were no incidents. YMMV. By the way, if you live in California they will tell you this is a terrible dangerous idea. Have you noticed those "known by the State of California to cause cancer"-labels on everything? I saw that notice on a lathe the other day. If everything causes cancer they should save the labels for things that don't cause cancer like warm distilled water. I think that's the only thing that will require a label.
