When the AC is being used, my basement tends to get about 5 degrees
cooler than the first floor. The basement is used for laundry, storage
and my workshop, so it doesn't need to be that cold.

Here's my idea: Cut a hole in my return trunk, near the floor, to
recapture the cooler air and send it back upstairs. I'd install a
filter and design it so it could be easily sealed up in the winter.

So, if this isn't a ridiculously bad idea, how would I go about
determining the correct size for the opening?