  Measurements of the thermal conductivity as a function of temperature and
magnetic field in the 2D dimer spin system SrCu$_2$(BO$_3$)$_2$ are presented.
In zero magnetic field the thermal conductivity along and perpendicular to the
magnetic planes shows a pronounced double-peak structure as a function of
temperature. The low-temperature maximum is drastically suppressed with
increasing magnetic field. Our quantitative analysis reveals that the heat
current is due to phonons and that the double-peak structure arises from
pronounced resonant scattering of phonons by magnetic excitations.
