One remark to Groth's post.
Fill the heatercore it with water... and use a small basin (or a bucket) with water, and put it in , leaving only the part you wish to desolder dry. The water in the bucket will maintain the rest of the heatercore cooler . Just filling it with water might not be sufficient.
My cores i just cut the pipes with my dremel, and gooped a couple of barbs. Worked
pretty good. It's another way to go.
Or, you can just cut them as close you can get, and then grind the rest with a power tool or some files.