You're supposed to use insulated pipe on the exterior. It's double wall and made of stainless steel, so it's expensive.
I spent more on the chimney pipe & parts than my wood stove cost, but it was a two story & I found the stove on ebay for 1/2 price.
I considered using single wall pipe, building a wood framed enclosure & packing it with a fireproof insulation, like Rockwool or vermiculite, but chose the $800 SS pipe in the end. I really think the cheaper solution would have been fine, but chickened out.
Oh, you're supposed to run the pipe closer to the exterior wall, and up through the eve instead of out past the edge of the roof.
I don't have the parts info here, or I'd include the brand name. Google will find it for you.