Putting some emphasis on correct technical terms, we should talk about temperature drift as in (a systematical effect) as in the question title in contrast to random fluctuations.
In the present circuit, resistor T.C. can be expected to be the most severe drift source, at least factor 10 larger than OP offset drift. It's promoted by a unsuitable instrumentation amplifier circuit that misses the chance to reduce the effect of common mode error. It should better refer to a standard true instrumentation amplifier circuit with the gain located in the first amplifier stage.
I presume that you separated amplifier from load cell drift in your measurement by shorting the load cell output terminals.