Electrical – Measuring power transformer capacity

I have a few small-ish unmarked power transformers. I would like to know what their ratings would be if I had the manufacturer's specifications. So far, I have determined that I can safely connect them to the mains without tripping a breaker.

For the voltage, I can use a DMM. However, an unloaded transformer produces a different reading than one with a load. Does the spec for a known transformer refer to the loaded or the unloaded reading?

I have heard about methods for approximating the transformer current capacity by measuring weighing them, but:

• the transformers are well under a pound, making a weight less
  accurate
• one type of transformer I have, for which I have 3 units,
  has two secondaries, and I would like to know the current capacity
  for each; the overall weight of the transformer will give only an approximate total power

I am about to experiment with an empirical approach in which I place power resistors of known values across the secondary in series with a DMM set for current reading, and then use an IR temperature gauge to watch how much the transformer heats up. The only problem here is I don't know what a typical maximum temperature would be.

Is this a viable approach? Any suggestions on making it accurate, such as an appropriate maximum temperature for the transformer under load?

I welcome answers with other techniques.