First of all did she tell the tech the wax was too hot?
Seeing as how the OP's wife suffered second degree burns (unlike you, I have no basis for contradicting facts contained in the original post), I think it's pretty safe to assume that the wife conveyed this message in no uncertain terms (whether verbal or otherwise). Were you thinking that the wife may have stoically suffered the pain and kept it a secret?
there are dozens of aesticians near her that were more qualified to do that.
There are? You know not only where the OP and his wife live or where she works but also how many aestheticians are in the area? You're also familiar with the relative qualifications of those aestheticians? That's pretty astounding (to the point of being utterly unbelievable)!
It is worth pointing out, however, that the OP's profile indicates he lives in Maine (a state that I doubt is teeming with aestheticians). Curiously, according to the Supercuts web site, there are no Supercuts locations in Maine (or in either of the Canadian provinces that border Maine). It appears there are six locations in New Hampshire (all in the Concord/Manchester area), so I supposed it's possible that the OP and wife live near the ME/NH border and that the wife commutes to the Concord/Manchester area for work.
By the way, whether or not there were other, subjectively better options is utterly irrelevant.
It is unlikely it will scar. It was probably a 1st degree burn, unlikely it was 2nd or 3rd degree.
Notwithstanding what the OP wrote.... Now you're making medical diagnoses over the Internet? Is there no end to your talents?! "No offense," of course. :-)