Lots of CFM fan power is required to move the warm air from the stove to the other end of the house and everywhere in between.
A quick and easy method, if you already have a forced air furnace is to cut a large hole in the cold air return of the stove and turn on the furnace fan. It will literally suck all the warm air from the basement and send it upstairs. If you want to use the furnace for heat or central A/C, close off the big hole. The hole in the side of the cold air return effectively renders all existing cold-air return ducts useless, as air, like water, will follow the path of least resistance (or air drag). I used a $20 permanent screen with removable window from Home Depot. Works great. I've switched to furnace only in less than a minute, after shutting down my stove for a couple of days, needing only to put the window back in.
But sending the warm air into the house area is only half the equation. You have to get the cold house air back to the stove to complete the circuit. I simply took off the basement door and had a major cold-air return coming down the steps. Works great, and it's a example of KISS (keep it simple, stupid)...or, if you'd rather, the easiest solution is usually the best.
If you don't have a forced air furnace, then you'll have to duct the air to the various parts of the house. It also means building or buying a heat jacket for your stove, and using one or more blowers to get the air around. Although heat naturally rises, it doesn't always flow up through floor openings from below. It needs to be forced up (ducted or blower), and a cold air return provided.
For what it's worth, I'm in the process of building a jacket for my Alaska stove and already have the top-of-the-stove duct connected to my furnace ducts, and cut into a living-room cold-air return and ducted that to the input side of my blower. It's a major victory in getting the upstairs warm. I hope to get the side jacket constructed and installed this weekend, pulling air from another living room cold-air return duct, and sending the heat into the furnace hot-air duct.