Filtering data on a known signal
The obvious answer: define a mathematical model of how the temperature affects your data, and use that model to remove the effect of temperature on your data.

Sorry, but with the amount of information you give on your data, the way your temperature affects it or any approach, this is the precisest possible answer.

I'd like to add that what signal processing defines as "filter" is probably not the tool you're looking for, unless you now the spectral properties of your data and your temperature.