The problem of phonon scattering by static strain fields due to biaxial wedgedisclination dipoles (WDDs) of finite length and circular wedge disclinationloops (WDLs) is studied in the framework of the deformation potentialapproach. The specific behaviour of the thermal conductivity, κ,is found for both defects. In particular, for WDDs the crossover fromT2to Tis predicted at low temperatures. For circular WDLs, κ(T) exhibits a minimum atsome temperature T*in the low-temperature range. Above T* κ ∼ T2(dislocation-like behaviour), while belowT*, one findsκ ∼ T−3.