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Where is this fuse? What is the brand and model number of your furnace?
So it's on the circuit feeding the furnace not in the furnace?
Ok so you have a short somewhere in the furnace wiring. Tracking it down can be a challenge. The first thing to do is check the wiring inside the box where the fuse holder is mounted. Make sure there are no bad connections (hot to ground or neutral). Is this an oil fired or a gas fired furnace?
Ok, once you check the wiring in the box the next step would be to disconnect the major components in the furnace; the main blower, the draft inducer fan (if it has one), does it have a control board or a fan center relay (disconnect the power to either one or both). Once all the components are disconnected try a new fuse. If it blows again then you have a short in the wiring. If it doesn't then re-connect the components 1 at a time starting with the board or the relay until you find which component blows the fuse.
That could just be due to the short and if you screwed the fuse in while the circuit was hot. It would be a good idea to replace the receptacle and if it doesn't have a service switch right there now would be a good time to install one. You should screw the fuse in then turn the power on. A switch right there would make this a lot easier