Does "triple-degree heat" mean the same as "triple-digit heat"?
The term "triple-digit heat" refers to ambient temperatures that equal or exceed 100 degrees Fahrenheit. The expression appears to be fairly new: a Google Books search turns up 23 unique matches for the phrase, but the earliest of these is less than twenty years old. from "Weekly Weather and Crop Bulletin," volume 88, issue 3 (2001) [quoted text does not appear in the snippet window]:
Tuscaloosa, Alabama measured 16 consecutive days of triple-digit heat from July 5–20. Pensacola, Florida saw 6 consecutive days of record high temperatures from July 15–20.
"Triple-digit heat" appears to be an offshoot of "triple-digit temperature[s]," which produces more than 50 matches and dates back to at least 1981. From Ray Scott, Underground Homes: An Alternative Lifestyle (1981) [snippet view]:
For 12 days in mid-July, 1980, the temperature reached 98 degrees Fahrenheit or above. The majority of those 12 days reached triple-digit temperatures.
The phrase "triple-degree heat" probably owes its existence to an illogical equating of "triple-degree" with "triple-digit." A temperature of 102 degrees Fahrenheit obviously has three digits (1, 0, and 2), but I can't think of any meaningful way to argue that it has three degrees.
Nevertheless, a Google Books finds six instance of "triple-degree heat," all from books published in the past fourteen years. The publishers implicated in these instances are respectable mainstream houses, although not all of the books themselves qualify as prestige volumes.
From John Vornholt, Buffy the Vampire Slayer & Angel: Seven Crows (Simon & Schuster, 2003):
An FBI agent tried to argue about jurisdiction with the local law mean, but he made little headway. In truth, none of them had much stomach for fighting the decision to get away from these heaps of sundered bodies, rotting in triple-degree heat.
"What's with the dead crows?" asked Riley, pointing to the black carcasses dotting the hillside like murdered exclamation points.
From Mary Herczog, Frommer's Las Vegas 2007 (John Wiley & Sons, 2006):
Except for minor-league baseball and hockey, the only consistent spectator sports are those at UNLV. For the pros, if watching Triple A ball (in this case, a Los Angeles Dodgers farm team) in potentially triple-degree heat sounds like fun, the charmingly named and even-better merchandized Las Vegas 51s (as in Area 51, as in alien-themed gear!) are an option.
From Lisa Kleypas, Sugar Daddy (St. Martin's Press, 2007):
The rich people are in great shape. It's the rest of us, the lovers of burritos and Dr Pepper and chicken-fried steak, who inflate the average. If you can't afford a gym membership in Houston, you're going to be fat. You can't jog outside with so many days of triple-degree heat and lethal levels of hydrocarbons in the air.
From Eileen Rendahl, Don't Kill the Messenger (Penguin, 2010):
Things had been tense in Sacramento and were only getting tenser. I couldn't wait until summer hit full force with its triple-degree heat that made short tempers into rages and put people in the mood to stab, shoot and throw punches at their loved ones and strangers alike.
From Miriam Pawel, The Union of Their Dreams: Power, Hope, and Struggle in Cesar Chavez's Farm Worker Movement (Bloomsbury Press, 2010):
Even the logistics of feeding more than one hundred deputies out in the fields all day, six days a week, became a challenge. Byrd requested Abba-Zaba bars, his favorite candy because the caramel and peanut butter confection didn't melt in the triple-degree heat.
And from Miriam Pawel (again), The Crusades of Cesar Chavez: A Biography (Bloomsbury Press, 2014):
After she [Librado's mother] died, he made a solo trip to California to scout out work. Then, in the summer of 1938, the family left the triple-degree heat of the Arizona desert and traveled to the temperate clime of Oxnard, California, where one of Cesar's aunts lived.
It also yields one instance of "triple-degree temperatures." From African Violet Magazine, volume 53 (2000) [snippet view]:
I don't know about you, but I am happy to say goodbye to a long, hot, Texas summer! The triple degree temperatures were a little later coming this year, but when they did arrive they stayed with us for awhile. Fortunately, we have not had a power outage in the violet house like we did last year so the violets have fared well.
It seems to me that every one of these instances would make more sense if "triple-digit" were swapped in for "triple-degree." But the authers either disagreed (Miriam Pawel clearly falls into this camp) or failed to realize that they had used the wrong word in the phrase.
As matters stand, the instances of "triple-degree heat" and certainly of "triple-degree temperature[s]" are probably too few to qualify those expressions as legitimate variants of "triple-digit heat" and "triple-digit temperature[s]." But if enough people make the same mistake, the legitimacy of "triple-degree" as a variant of "triple-digit" will gradually become stronger—because that's the way language works.
Meanwhile, if I were one of the mainstream publishers whose names appear in this answer, I would say, "Come back, copy editors—all is forgiven!"