Here we go, just grabbed a picture of the top!
Looks like that might be class A pipe going thru the roof. If so, your cheapest solution is to attach this shield to the single-wall stove pipe where it gets closer than 18" to combustibles.
http://www.amazon.com/Imperial-Group-BM0133-Adjustable-Shield/dp/B000DZQR3Q
Keep an eye on the pipe. That looks like cheap hardware stove stove pipe.Watch out for any sign of tiny holes developing, especially where there is rust and replace all the pipe at that time. Note that the crimped edge is supposed to be on the bottom edge of the pipe (toward the stove).