  We show how the correlation between the thermal Sunyaev Zel'dovich effect
(tSZ) from galaxy clusters and dust emission from cosmic infrared background
(CIB) sources can be calculated in a halo model framework. Using recent tSZ and
CIB models, we find that the size of the tSZ x CIB cross-correlation is
approximately 20 per cent at 150 GHz. The contribution to the total angular
power spectrum is of order -2 \mu K^2 at ell=3000, however, this value is
uncertain by a factor of two to three, primarily because of CIB source
modelling uncertainties. We expect the large uncertainty in this component to
degrade upper limits on the kinematic Sunyaev Zel'dovich effect (kSZ), due to
similarity in the frequency dependence of the tSZ x CIB and kSZ across the
frequency range probed by current Cosmic Microwave Background missions. We also
find that the degree of tSZ x CIB correlation is higher for mm x sub-mm spectra
than mm x mm, because more of the sub-mm CIB originates at lower redshifts
(z<2), where most tSZ clusters are found.
