Compensation formula for temperature changes on a load cell

I’m looking for a formula to apply a compensation to the voltage output of a load cell that produces an error with changes in temperature. See the curve below of samples of temperature changes (yellow) and voltage changes (blue) over time. The load cell has a static weight that does not change over the sampling period so the changes are only attributable to the variation in temperature. Note that the axis for the output voltage has been adjusted so that the change is easier to see, in reality the voltage variation is in the order of 3 – 5%, our compensation formula has to get that error range down to about 1%. Also note the temperature sensor is attached to the load cell so is experiencing the same temperature as the metal in the load cell, and the load cell is supposed to be temperature compensated (wheatstone bridge arrangement) but is still impacted by temperature changes.

There is clearly an inverse relationship that is a derivative of temperature change (the faster the temperature changes the bigger the impact on the voltage error) as dTemp / dTime. Problem here is that the resolution of the temperature sensor we use isn’t very granular, and as the compensation formula will need to cumulatively add or subtract from the actual value (I’m assuming), the inaccuracy of the compensation will accumulate over time leading to larger errors / drift.

I’m sure there is a better way to apply the compensation (and code it up in the firmware) so that we can compensate based on the relationship displayed in the graph below (and without accumulating errors due to the compensation) however my calculus isn’t good enough to work it out.

Any ideas how to best approach this compensation question?