there are a number of different invisible threads on the market- some are like fish line- melt if an iron hits them- and are pokey when they break (like the tag in that shirt that drives you stark raving mad poking you)
others do not melt- hold up to laundering- and are soft-
another option is silk thread in a neutral color-light gray or cream for light fabrics, dark gray/natural for darker fabrics work well- blend in and about disappear.
visit thread sites (like Superior Threads, Atlanta Thread company, Sulky...to name a few)
they (especially Superior threads) have free sheets you can print off telling you about all the different threads - what they are good for- what needle to use- what they are good for---