Like others have said, it could be in the ducts. It also could have died in the "squirrel cage" blower motor. If it isn't in the engine bay at all or under the car, I would start taking apart the dashboard to get to the blower motor.... do you do your own car work? If not, I would take it to a mechanic to get the mouse out. I am not one who would drive around breathing a rotting animal.....
This!
Picture young 20 year old me, in my tiny hatchback, and something had died in that car about 4 days before, and it was a hot day.
I pull to the side of the road, get out and open the doors, and try to look / find what is wrong. I sit in the driver's seat and turn on the fans to help blow more air around. when...
fwpttt -- mouse parts flew past me out of the ventilation shaft. (the vent went from the dash, and through an open port to the door vent....) but with the door open, that was a nice round hole that part flew at me out of.
I will never forget that smell. Best of luck to ya.