Hi Glenn,
In a repair such as the one viewed, referred to as a bonded insert, there is the need to have some foundation of some sort to tie the insert to the rest of the carpet. One of the more common ways is to use conventional seam tape or something similar. Then the tape is glued to the carpet on the floor and then the insert is glued to the tape and hopefully sealed to help bond the piece further, (this helps to keeps any hinge effect from occurring which will show the cut area or the seam).
In this case, the conventional seam tape has nothing to melt the adhesive on it since a conventional seam iron will not work well or will not be practical to use, so it is simply used as a foundation to hold the pieces together. This is why a glue gun is usually used to hold everything together.
It is a fairly common practice for some to use a steam iron, (the type used for ironing clothes), where one melts the adhesive on the conventional seam tape. This would certainly not be a practical thing to do with tufted carpet because it could easily cause other damage, yet some will still try to do this. They will try to melt the tape under the carpet by placing the iron on top of the carpet, usually with a towel of some sort. This is not a good idea.
Of course, a very practical way to do a repair like the one viewed would be with the Kool
Glide. This system is designed to work with such a repair and works very well. This along with sealing of the edges, with a glue gun and Kool Glide adhesive sticks, will allow everything to fuse together and this helps to minimize the seams and helps to keep the normal flexing of the inserted area from occurring in a way that may highlight the seams.
You may want to try one of these repairs. There are several that have tried it by watching and learning from others on this board and have had great success in doing so. Try it with some remnant pieces of carpet and you may want to add this service to your arsenal of things you perform for the clients you have.
I hope this helps a little.
SA