Furnace or boiler, air ducts, forced hot water, or steam?
There is a panel somewhere on the 'box' which you can safely open, or a door on older iron boilers. Locating a dead animal in air ducts can be time consuming but they can come apart (helps if you can tell where the smell is coming from), or a pro can snake a camera down them. It could also be in the vent pipe that goes outside (roof, side wall, chimney).
I have a feeling that many people just let them dessicate... the trouble is you don't know if it's small like a mouse or bird, or larger, which will take longer.