Note that the datasheet for an ADC only discusses errors from linearity, step size, ...

It does not cover the calibration relating to the voltage reference. And how the voltage reference may be affected by temperature changes.

So with four ADC at different locations, you may need to measure four temperatures too.

Of course, you may have to do that anyway, to keep track of variations with the load cell - and any electronics between load cell and ADC - while the temperature is varying.

You supply voltages may also vary with temperature - and different types of voltage references will be differently affected.