Following is a summary of a method that I posted on another forum:
As long as the internal temperature doesn't rise above 90°C with the intended load, then it should be okay. It's quite easy to determine internal temperature based on the change in DC resistance of the primary winding. The DC resistance of the winding changes with temperature, and for copper it's 0.0039 ohms per ohm per °C. So, simply measure the primary winding resistance before powering up the transformer and also make note of the room temperature. We'll call this the cold resistance Rc and cold temperature Tc. Then run the transformer under load for about 45 minutes, then disconnect power and measure the resistance again. We'll refer to this resistance as Rh. The internal temperature is then:
Th=Tc+Rh/(0.0039*Rc)-1/0.0039
For doing the test, it may be more convenient to determine in advance, the resistance value that corresponds to 90°C. So, then it's simply a matter of making sure that the winding resistance doesn't exceed this value. The formula is:
Rh=Rc*(0.0039*(Th-Tc)+1)
So, let's say you measure the transformer primary at 20°C (room temperature), and get a value of 150 ohms. Applying the above formula, Rh comes out to be 191 ohms. So, as long as the hot resistance of the primary never exceeds 191 ohms you should be okay.
To put it even more simply:
The hot resistance of any transformer winding should never be more than 1.27 times the cold resistance.
You'll want to start with a conservative load, and as long as the operating temperature stays below 90°C, then you can increase it, and run the test again. If you'd rather put the full load on it right away then you should take frequent resistance readings to make sure that the transformer doesn't go above a safe temperature.
I recommend measuring the primary winding resistance because its temperature rise will account for all losses, will usually be the inside winding which is most critical for temperature, and will generally have a resistance that's high enough to measure with reasonable accuracy.
I should also mention that 90°C is too hot to touch, and so you may consider that to be pushing things a bit too hard. However, this is referring to the internal temperature, not the surface temperature of the transformer, which should be somewhat cooler. However, if the surface is ever too hot to touch, then you may want to derate it a bit, even though virtually all modern transformer insulation is designed for a minimum of 90°C.