A system current sensor module can accurately sense or measure system current flowing through a sense current resistor by shunting current through a gain-setting resistor and using an amplifier to measure a resulting voltage, with an output transistor controlled by the amplifier controlling current through the gain setting resistor in a manner that tends to keep the amplifier inputs at the same voltage. The resistors can be thermally coupled to maintain similar temperatures when a system current is flowing. The thermal coupling can include conducting heat from a first resistor layer carrying the current sense resistor to a thermal cage layer located beyond a second resistor layer carrying the gain-setting resistor. This preserves accuracy, including during aging.