_Robert This is a topic I need to cover in more detail soon. The print setup you describe should work great, an enclosure won't be needed but also should do no harm.
The parts should be annealed in dry air with the supports still attached to the part. I anneal Nylons around 185 F, but you might get better results a little hotter. Once the part is fully heated it does not take that much time before you can slowly cool it. A couple hours of heat is all it takes for lowers and similar sized parts.
The only complexity in the process is shrinkage. You should print some test bars with the same settings as the final part, and measure them on all axis prior to and after annealing. Absolute material shrinkage is usually very low, but the lines tend to compact effecting the Z axis and one of the horizontal axis depending on infill. Keeping the results in mind you can then scale each of the axis of the final part.
On large or long skinny parts you might get some warping, and it's hard to combat that easily. But for smaller parts it should not be an issue.