At my first internship, for a new project, the company sourced around five (somewhat dodgy) power adapters with similar specs. The lead engineer had me open all of the units, apply polyester tape to the transformer winding, output cap(s), output diode, and primary-side switching transistor. (This was to give each component roughly the same emissivity, around 0.95-0.99.) Then, I ran each power supply at the same load for about an hour each. After one hour, I checked the temperatures of each of the aforementioned components with an IR gun. We compared the temperatures of the five units and the chose the power adapter with the best overall temperatures.
If testing at room temperature (25°C) like this, with the power adapter housing cracked open, I'd suggest to ensure that following temperatures are met:
Transformer: 85-90°C (max.)
Output diode, primary-side transistor, bridge rectifier, etc: 85°C (max.)
Output capacitors(s) and primary bulk cap:
Should be 105°C rating on the label. If it's 85°C, don't even bother. Check the manufacturer datasheet to find the endurance rating (as below):
~50°C (max.) for 2,000 hour rated cap
~60°C (max.) for 5,000 hour rated cap
~70°C (max.) for 10,000 hour rated cap
These temperatures would give you about 30,000 - 35,000 hours life at full load and at max ambient of 40°C. Obviously, it's up to you to determine what is "reliable enough".
Those are just ballpark suggestions. And again, the temperatures above are assuming you are measuring component temperatures at room temperature ambient. Safety-wise, the transformer is most critical. Temperature testing won't tell you if the transformer is constructed correctly, but the farther away the temperature rating is from the enamel rating of the wire (usually 130°C), the better. The components will probably run at least 10°C hotter in the enclosure, plus add another 15°C to account for a typical worse case ambient of 40°C.
Also check that the Y-caps (usually blue ceramic disc capacitor) are Y1 or Y2 type. It should be printed with various symbols like VDE and other agencies. If it just says "102 1KV" that's probably not a safety rated capacitor.