Hi Derun93,
I personally think that wouldn't work, I'm afraid, but there's nothing to stop you simulating it in a free program like LTSpice to see what happens, and there are many other free simulation programs, if you're interested the forum section called "Software problems, hints and reviews"
https://www.edaboard.com/forums/14/
or possibly also in PCB Routing Schematic Layout software and Simulation
https://www.edaboard.com/forums/15/
I don't remember exactly which/who, but there are at least a couple of threads regarding simulating the LM35, and/or finding a model for a simulator which could help.
"or if I just connect ground leg to the ground, what temperature sensors measure?" I think it has already been mentioned in this thread: the
LM35 plastic/silicon body is the temperature sensor, not the +V and -V pins, the +V and -V pins just power the integrated circuit so it can output the 10mV per degree Centigrade through the Out pin.
Unless some-one offers a better suggestion, I'd just connect the +V of each of the 4 LM35s to the top of the first battery, and the -V/GND pins of the LM35s to the -V of the bottom battery, that's what I'd recommend. ...I say so because you said you don't want to use an external power supply.
Because I've never used the LM35 powered by more than 5V, even if it can be powered up to 30V according to the datasheet (it says 4 to 30V), I'd also pay attention as to whether ~18V makes it a little hot, and a dropping resistor or some 5.1V Zener diodes would be helpful.
Datasheets are a PITA for newbies like you and I, you have to decipher them by re-reading them until the graphs and descriptions, and obscure clues you glean from application hints or the "electrical characteristics" sections make the device you are using comprehensible.
Good luck!