You need to remove the squirrel from your furnace carefully to avoid setting the animal loose inside your home or being bitten. You do not want to allow the squirrel to die inside your home due to the odor and high potential for exposure to harmful diseases and bacteria.
Turn off the Furnace
Turn your heater and furnace off immediately if you believe there is a squirrel or other animal in your furnace. You do not want to have it accidentally turn on and turn your squirrel into a crispy critter. Burned, rotting animals can pose a significant potential health problem within your home. Dead animals can be be very unpleasant to clean out and remove safely.
Contact a Professional
Contact a wildlife or pest control professional to determine the most efficient and effective way to have the animal removed from your furnace without anyone getting bitten or the squirrel getting loose in your home. In some areas, you may be able to contact your county animal control office and have animal control officers come professionally remove the animal from your furnace as a public service. Be aware that trying to remove an animal yourself without using any expert techniques or equipment can be very dangerous.
Trapping
Set traps for your squirrel to remove it from your furnace and home completely. Live traps can be set in your furnace room near the door of the furnace so that the squirrel can leave the furnace and be humanely captured then removed alive from the home. Otherwise, you can use poison bait and snap traps to kill your squirrel; however, you want to ensure the squirrel dies somewhere you can easily locate it and remove it.
Prevention
Removing a squirrel from your furnace is not something you want to have to do more than once. Locate the squirrels entry points to your home and cover them with hardware cloth or a metal grate that will prevent squirrels from re-entering your home in the future. If you have large trees surrounding your property, you may need to cut off branches to limit access to your home.