Small ones self-heat due to the primary self-excitation current even when no power is being drawn from the secondary. I'm playing with a 40VA (120VAC primary) transformer as we speak, and it draws 6W (14VA) just plugged in with no load. It gets up to about 25 deg C rise above ambient when left plugged in for 24 hours.
Fully loaded, it gets even hotter, but the overall efficiency increases to about 75%
the efficiency depends on the core used. With CRGO core and little higher turns/volt, one can expect 85%. the iron loss , as I mentioned, the core would be responsible..
You can measure the primary and secondary resistance. You can then calculate the copper loss. That will be added to the iron losses, which are fairly constant and do not vary much with load.