It looks like Ich, but is it? Ich doesn't just go away, and there are other white spot parasites with poorly known life cycles. If you leave Ich untreated, the fish go away, not the parasite.
Neoichthyophthirius schlotfeldti is an Ich relative that is becoming more and more common on fish farms, and that reproduces on the fish, and not in the water column. It can reproduce at up to 34 degrees C, so it may be what aquarists thought was the heat resistant Ich that is unbothered by the treatment
@Fishmanic suggests. It may respond to malachite green treatments. That, I am frankly uncertain of.
I had some harlequins with something like it years ago. It flared up and disappeared after I treated for Ich, but it never vanished and never killed the fish. It always came back. It moved very slowly, and had very large cysts. We all want cut and dried answers, but this one is around, and is complicated because unlike Ich, we haven't really gotten a handle on it. It just seems weird that it strikes your new fish but vanishes right after without killing. That isn't Ich behaviour.