080814-1104 EST
More information on the Leviton 7899-W GFCI. I am only using this particular device in tests because it available, not too expensive, and may be representative of other units. It would be useful if someone else would analyze something like a Hubbell.
Another thread titled Overheating of GFCI Breaker had some comments that the breaker being hot might be due to the electronics. This seemed unlikely. Thus, a couple experiments on the 7899 since I do not have a GFCI breaker and do not know what brand was in the panel.
First, what is the power dissipated in the electronics. With the GFCI set by applying 120 V to the input and pushing the RESET button the electronics are energized. With no other load I measured the input current with a Fluke 27 and 87 and the results were different but generally in the ballpark of each other. The higher reading was about 8 MA and this means about 1 W at most. One watt internal will not produce much temperature rise on the outside surface of the GFCI.
Second test. Measurement of the power dissipation from 18.5 A flowing thru the GFCI. This was done with the GFCI preset, a 5" #12 wire shorting from the hot to neutral output screw terminals, and applying an adjustable input voltage to hot and neutral input to obtain 18.5 A. The voltage was measured between the screw heads of the two input terminals. Results I = 18.5 A, V = 0.129, P = 18.5*0.129 = 2.38 W, and R internal = 0.129/18.5 = 0.007 ohms. Obviously this produces more power dissipation than the electronics, and there is no power dissipated in the electronics at this very low input voltage.
I am working on photos to show the construction of the 7899.
.