Electronic – Why can’t I measure resistance when there is current on the potentiometer

Most likely you are reading the detected voltage into a computer or MCU. The slope of the voltage graph with respect to temperature should be of little concern because it is so easy to "invert" the detected temperature by subtracting the reading from a constant that is the equivalent of the 5V level in your system.

100mA pulsed at 50% duty cycle for 16 hours equates to 800mAh. If your battery had much larger than 800mAh capacity then its voltage might not drop much, and might even increase if its temperature rose or it had previously been under heavy discharge. However if you keep the circuit running for long enough the battery voltage should start dropping.

The 'ground' in your circuit is just a reference point. The only path the current can take is from battery +ve to battery -ve. Current in the wire between the load and 'ground' is flowing towards 'ground', and current in the wire from 'ground' to battery -ve is flowing away from 'ground', but no current can flow into or out of the 'ground pin' itself because there is nowhere for it to go. At all points in the circuit you should measure the same current flowing and always from battery +ve to -ve (eg. when measuring current in the wire between 'ground' and battery -ve, the meter's positive lead would be connected to 'ground').

Your diagram perfectly illustrates what the current should be doing. However it does not show the complete circuit with all components (load switcher, ADC etc.). Are you sure that this extra circuitry is not somehow feeding current into the battery? If you find that battery voltage continues to rise rather than drop then you will have to analyze the entire circuit to find out why.