Recent works have shown promising results in in vivo temperature estimation using diagnostic ultrasound. By applying speckle tracking algorithm on the M2D images taken by a diagnostic probe positioned in the fenestration of a Dual Mode Ultrasound Array (DMUA), localized temperature changes during sub-therapeutic High Intensity Focused Ultrasound (HIFU) operation can be detected. However, interference from natural motion and deformation of the tissue could result in severe errors in the estimated temperature profiles. Two-dimensional filtering inspired by the bio-heat equation was shown to partially mitigate these effects, but it is ineffective when the spatial frequencies of the deformations are within the same bandwidth of the temperature-induced strains. We present results of a new adaptive technique which is capable of largely suppressing the interference without sacrificing the dynamics of the temperature change. The method is based on finding points with strong deformation induced strains outside the targeted region before the therapy starts and training an adaptive filter with the signals from these points as it inputs. During the therapy, the strain data from selected points and trained coefficients are used to suppress the effect of natural motions using a spatial interference cancellation filter.