1. A method of determining a strain at a member in a borehole, comprising: sending a pulse of light along a fiber optic cable extending along the member; receiving a signal in response to the pulse of light related to a temperature at a distance along the fiber optic cable; and using a processor to: select a first subspace of a measurement space of the received signal, the first subspace characterized by a step having a selected step size; estimate an error for a filter corresponding to the first subspace; adjust the step size when the estimated error meets a selected criterion; select a second subspace characterized by a step having the adjusted step size; apply the filter corresponding to the second subspace to the received signal to obtain a filtered temperature signal; and apply the filtered temperature signal to a strain measurement obtained at the member to obtain a temperature-corrected strain measurement at the member.