Ran some controlled tests using a contact K-thermocouple with simulated charging voltage regulated at 13.8 volts and ambient temperature stabilized at 77° F.
After adjusting the fuel level sender resistance to 88 ohms, so the fuel level gauge indicated FULL, the net current flow through the gauge circuit measured 0.143 amp while the temperature of the ceramic resistor on the back of the fuel gauge stabilized at 93.2° F (barely warm).
Readjusting the fuel sender resistance to 1 ohm, so the fuel gauge indicated EMPTY, the net current flow through the gauge circuit increased to 0.291 amp while the temperature of the resistor increased and then stabilized at 123.8° F (
quite warm to the touch and similar to what you measured independently).
So, now we have some quantitative data. The fuel gauge and resistor DO GET WARM! It's normal! So, there's no cause for concern.