A few years ago a hummingbird came into our house, and flew up into one of the recessed skylights. He just stayed there hovering, and trying to fly up out of the skylight. I thought "I'll give him 10 minutes before he runs out of energy." An hour later, he was still hovering. I'm amazed that he could keep going for so long.
I put a squeegee on a long pole (cathedral ceiling), and put that up next to him. He perched on the squeegee, I lowered it and stuck it out a window and he flew away.
BTW, no action yet on the snap trap. I haven't heard any noise, but I expect the animal is still there. I'll have to come up with a plan B soon.
I'm guessing that turning on the furnace will not kill the mouse, but it might drive him towards the snap trap. Will try that now.