Not sure how a bridge circuit can have impedances that are close to balanced unless you employ a variable impedance resistor in the bridge? Or perhaps a ladder of resistors in series that are shorted by transistors as needed?
Yes, that's how you will need to balance your bridge (Zeroing) for the temp you want to establish as reference. Ten turn precision pots are regularly used for that. Another way is to set an offset voltage level added to the diff amp. If the signal is converted to digital, corrections can also be done by adding or subtracting a "DC voltage" value to the samples to compensate for the difference and zeroing the bridge.