ANENG AN870, AN8009 and Zoyi ZT-Y go down to 0.01 ohms very accurately, and use 3.2V for the voltage output. All of these are around $20-$30 at AE.
The ZT-5566 is a slightly better ZT-Y. It's a benchtop with bluetooth speaker, so you'll pay a few times more than the others.
Not sure why you need to consider the resistance voltage? The meters I mentioned are roughly 0.4 mA output current (when tested using another multimeter in its mA current range). If this is something you really need to know, say something and I will test them using your sample resistor size.
What are you expecting for graphing exactly? An oscilloscope? Historical Tracking? Just a bar graph on the display?
BTW do you need a thermal camera for your troubleshooting? The Tooltop ET13s IR+DMM does voltage graphing historically on screen in the multimeter mode. However this meter has poor low resistance performance. Not to be trusted under 10 ohms (that bad). On the good side, the diode output voltage is nearly 4V.