I use one of these AOYUE 936 except I've swapped the point tip for a 1.8mm (I think) flat one. I usually do 350C just because it is what I do my through-hole at.
For building in bulk I use the toaster oven with solder paste. Take it up to 140C, turn it off for a minute or two until the temp holds, then turn it up until it reflows fully which is about 200-210C.
Soldering the TC amp is all about patience and preparation and a very small diameter solder.