Swamp Cooler ducting help

[930dreamer]

I need to install a swamp cooler at the shop and need some ducting help. Unit will be on the north wall, is it better run the trunk from the cooler on the outside and up/in, or inside the building and up.
Cooler specs are industry standard 6500/4330 high/low. Shop is 3200 sq ft and no insulation. Outlet opening is roughly 20"x20". It's hotter inside now then out.

I called a local sheet metal company and they said just install through the wall, so that's what I did. Here's a video;