  We investigate the weak lensing corrections to the cosmic microwave
background temperature anisotropies considering effects beyond the Born
approximation. To this aim, we use the small deflection angle approximation, to
connect the lensed and unlensed power spectra, via expressions for the
deflection angles up to third order in the gravitational potential. While the
small deflection angle approximation has the drawback to be reliable only for
multipoles $\ell\lesssim 2500$, it allows us to consistently take into account
the non-Gaussian nature of cosmological perturbation theory beyond the linear
level. The contribution to the lensed temperature power spectrum coming from
the non-Gaussian nature of the deflection angle at higher order is a new effect
which has not been taken into account in the literature so far. It turns out to
be the leading contribution among the post-Born lensing corrections. On the
other hand, the effect is smaller than corrections coming from non-linearities
in the matter power spectrum, and its imprint on CMB lensing is too small to be
seen in present experiments.
