They are in the news once again. (Here is a free access summary.) I have had time to read the article just yet, but this research seems to be taking a slightly different tack, namely using two different sizes of polymers which favorably interact through pi-pi bonds. In essence, one is plasticizing the other.
I've mentioned this category of materials in the past(1 and 2) and have always been underwhelmed. I don't see this being much different.
"Heat and heal" is a common characteristic of most thermoplastics, as heating allows for flow - interpenetration of the two surfaces. HDPE pipe is joined like that, potato chip bags are sealed like that... It's not wonderful new technology.