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Planets can emit polarized thermal radiation, just like brown dwarfs. We present calculated thermal polarization signals from hot exoplanets, using an advanced radiative transfer code that fully includes all orders of scattering by gaseous molecules and cloud particles. The code spatially resolves the disk of the planet, allowing simulations for horizontally inhomogeneous planets. Our results show that the degree of linear polarization, P, of an exoplanet's thermal radiation is expected to be highest near the planet's limb and that this P depends on the temperature and its gradient, the scattering properties, and the distribution of the cloud particles. Integrated over the disk of a spherically symmetric planet, P of the thermal radiation equals zero. However, for planets that appear spherically asymmetric, e.g., due to flattening, cloud bands or spots in their atmosphere, differences in their day and night sides, and/or obscuring rings, P is often larger than 0.1%, in favorable cases even reaching several percent at near-infrared wavelengths. Detection of thermal polarization signals can give access to planetary parameters that are otherwise hard to obtain: it immediately confirms the presence of clouds, and P can then constrain atmospheric inhomogeneities and the flattening due to the planet's rotation rate. For zonally symmetric planets, the angle of polarization will yield the components of the planet's spin axis normal to the line of sight. Finally, our simulations show that P is generally more sensitive to variability in a cloudy planet's atmosphere than the thermal flux is, and could hence better reveal certain dynamical processes. [ABSTRACT FROM AUTHOR]