What brand of thread are you using? I use YLI nylon monofilament in my domestic machine, both top and bobbin, with no problems. I believe the only other *great* brand of nylon monofilament thread is SewArt.
Here is a link to a WONDERFUL article about invisible thread on the QB:
http://www.quiltingboard.com/resources/article-87.html
I haven't read through the entire article in detail, so I will mention here some of the things I do to make invisible thread work for me. (1) Loosen upper tension because nylon stretches under tension. (2) Wind bobbin slowly so thread is not stretched on the bobbin. Also fill bobbin only 3/4ths full because nylon can distort the edges of the bobbin if you overfill. Metal bobbins are less likely to distort than plastic bobbins, but still do not fill completely. (3) I have never had a problem with YLI nylon melting under an iron. (4) I have tried some polyester threads and found them more *visible* than YLI nylon. There may be a polyester thread that works just as well, but I haven't found it yet. (5) SewArt nylon monofilament is supposed to be slightly preferable to YLI because it is more of a matte finish; YLI has a little shine to it. SewArt wasn't available when I bought mine, which is why I went with YLI. (6) I place the net over the cone, then run the thread up through the center of the net. On my domestic machine, the cone is placed in a glass jar behind the machine and I run the thread through an "outrigger" before threading as usual. My "outrigger" is just a plastic bar about 6 inches long with a big hole in one end that slides over the spool pin and a small hole in the other end through which I run the thread. Most people use a cone holder instead. The point is that the cone thread needs to feed upwards out of the cone into a "guide" that will position it reasonably for feeding through the machine.
Hope this helps!