They aren't designed to handle 125% of their nameplate rating. They are designed to operate up to a specific temperature before the insulation begins to break down, which will lead to failure of the "boom" variety. Usually, distribution dry-type indoor units are rated 220 C. In 40 C ambient, that allows for 40 + 150 C rise = 190 C with a 30 C allowance for unavoidable hotspots. Generally, engineers will rerate 1% for each 1 C below/above 40 C ambient. There are some guidelines in IEEE if you are so inclined to read further. If you overload a transformer, its temperature rise will be higher than the nominal 150 C, but it is difficult to predict how much more temperature rise will be observed for operating above nameplate ratings.
Likely the NEMA design criteria referenced in Post #3 is a good nugget of info. I would never rely on that in a formal capacity or in a technical report, but it is certainly worth mentioning while sitting around the table and talking through the specific problem. Otherwise, my approach is to consult with the manufacturer to see what they recommend, understanding that operating outside those boundaries will open me to liability if I make a recommendation to do so. If that makes my approach conservative, so be it.