No reamer yet. I bought my barrel about three years ago from PacNor. Just a heavy center turned blank. I had no luck finding someone to sell me a reamer. I was thinking of trying to make a pull through type myself. Seems like that would be a nice way to come up to headspace.That kind of thing is why this is a long long project. and I only get back to it now and then.
I think my fixture may act as a heat sink somewhat. But may just turn out to be a waste of time other than improving my sorry ass lathe skills.