Several of the current and next-generation cosmic microwave background (CMB) experiments have polarimetric capability, promising to add to the finesse of precision cosmology. One of the contaminating Galactic foregrounds is thermal emission by dust. Since optical interstellar polarization is commonly seen, from differential extinction by aligned aspherical dust particles, it is expected that thermal emission from these grains will be polarized. Indeed, in the Galactic plane and in dark (molecular) clouds, dust emission in the infrared and submillimetre has been measured to be polarized. It seems likely that the faint diffuse cirrus emission, of more relevance to CMB experiments, will be polarized too. We discuss how well the amount of polarization of this component can be predicted, making use of what is known about optical (and infrared and ultraviolet) interstellar polarization and extinction. Some constraints on the alignment of the carrier of the dust-correlated anomalous microwave emission can be made as well.